Can You Pray Tarawih while Travelling?
Question

Since the rituals of Ramadan are very special for every Muslim who becomes obviously religiously active. I would like to ask about a traveller’s Tarawih prayer.
Praise be to Allah.Virtues of Tarawih prayer
Tarawih prayer in Ramadan is qiyam al-layl , and Allah praises those who do it in the verse (interpretation of the meaning): 
“They used to sleep but little by night [invoking their Lord (Allah) and praying, with fear and hope]” [al-Dhariyat 51:17] 
The Prophet (peace and blessings of Allah be upon him) prayed qiyam in Ramadan and at other times, and he did not stop praying qiyam whether he was travelling or not. 
Ibn al-Qayyim (may Allah have mercy on him) said: 
“He (the Prophet (peace and blessings of Allah be upon him)) did not stop praying qiyam whether he was travelling or not. If he was overcome by sleep or pain, he would pray twelve rak’ahs during the day.” (Zad al-Ma’ad, 1/311) 
Al-Bukhari (945) narrated that Ibn ‘Umar (may Allah be pleased with him) said: The Prophet (peace and blessings of Allah be upon him) used to pray qiyam al-layl atop his camel when he was travelling, no matter what direction it was facing, gesturing to represent the movements of the prayer, apart from the obligatory prayers, and he would pray Witr atop his camel. 
And al-Bukhari narrated that Salim ibn ‘Abd-Allah ibn ‘Umar (may Allah be pleased with him) said: ‘Abd-Allah ibn ‘Umar (may Allah be pleased with him) used to pray atop his mount at night when he was travelling, and he did not care what direction it was facing. Ibn ‘Umar said: The Messenger of Allah (peace and blessings of Allah be upon him) used to pray nafl prayers atop his camel, no matter what direction it was facing, and he would pray Witr like that too, but he did not pray the prescribed prayers like that.
Offering Sunnah prayers while traveling
The nafl prayers that the traveller may omit are the regular Sunnah prayers before and after Zuhr and the regular Sunnah prayers of Maghrib and ‘Isha only. As for all other regular Sunnah and nafl prayers, they are prescribed for both travellers and non-travellers. 
Muslim narrated in his Sahih (1112) that Hafs ibn ‘Asim ibn ‘Umar ibn al-Khattab said:
“I accompanied Ibn ‘Umar on the way to Makkah. He led us in praying two rak’ahs of Zuhr prayer, then he left and we left with him until he came to where his luggage was. He sat down and we sat with him, then he looked towards the place where we had prayed, and he saw some people standing and he asked, ‘What are these people doing?’ I said, ‘They are praying voluntary prayers.’ He said, ‘If I wanted to pray (nafl or Sunnah prayers) after the fard prayer I would have completed my prayer (i.e., not shortened it).’ O son of my brother, I accompanied the Messenger of Allah (peace and blessings of Allah be upon him) whilst travelling and he did not add anything to these two rak’ahs until Allah took him (in death); and I accompanied Abu Bakr and he did not add anything to these two rak’ahs until Allah took him (in death); and I accompanied ‘Umar and he did not add anything to these two rak’ahs until Allah took him (in death); and I accompanied ‘Uthman and he did not add anything to these two rak’ahs until Allah took him (in death). And Allah says (interpretation of the meaning): 
‘Indeed in the Messenger of Allah (Muhammad) you have a good example to follow’ [al-Ahzab 33:21].” 
The phrase “If I wanted to pray (nafl or Sunnah prayers) after the fard prayer I would have completed my prayer” means: If I had chosen to pray nafl prayers, then completing my obligatory prayer as four rak’ahs would have been dearer to me, but I do not think I should do either, because the Sunnah is to shorten the prayer and omit the regular Sunnah prayers too. 
Offering Tarawih while travelling
The scholars of the Standing Committee for Issuing Fatwas were asked: 
What is your opinion on travellers – is it better for them to pray Tarawih in Ramadan or not? (They are shortening their prayers) 
They replied: 
Praying qiyam in Ramadan is Sunnah, and was established by the Messenger of Allah (peace and blessings of Allah be upon him). Hence the Companions (may Allah be pleased with them) took that from him and followed him in that, and it has persisted until our own time. It is proven in al-Sahihayn from the hadith of ‘Aishah that he (peace and blessings of Allah be upon him) prayed Tarawih for several nights and they prayed with him, then he stayed home and prayed in his house for the rest of the month, and said: “I was afraid that it might be made obligatory for you and you would not be able to do it.”
In al-Bukhari it is narrated that ‘Umar united the people behind Ubayy ibn Ka’b and he led them in praying Tarawih. And it is proven in al-Sahihayn from the hadith of Abu Salamah ibn ‘Abd al-Rahman that he asked ‘Aa’ishah (may Allah be pleased with her): How did the Messenger of Allah (peace and blessings of Allah be upon him) pray? 
She said: He did not do more in Ramadan or at any other time than eleven rak’ahs . He (peace and blessings of Allah be upon him) traveled in Ramadan, including when he travelled to conquer Makkah. He (peace and blessings of Allah be upon him) set out on the tenth of Ramadan in 8 AH. Ibn al-Qayyim said: He (the Prophet (peace and blessings of Allah be upon him)) did not stop praying qiyam whether he was travelling or not. If he was overcome by sleep or pain, he would pray twelve rak’ahs during the day. Thus it is clear that if they pray it whilst travelling they will be following the Sunnah.” (Fatawa al-Lajnah al-Daimah, 7/206) 
To sum up, praying Tarawih is mustahabb for the traveller as for the non-traveller, because the Prophet (peace and blessings of Allah be upon him) persisted in praying qiyam al-layl whether he was travelling or not. 
We ask Allah to help us and you to obey Him and attain His pleasure. 
And Allah knows best.