Each course teaches students, who must be 18 or older when attending, about GCHQ's work to combat cyber-threats and helps them develop their "cyber-skills".
The schools are held at four sites in the UK, an increase from two last year.
The expansion was made following high demand for places, GCHQ has said.
One of the schools, Cyber Insiders, will give participants the chance to learn from a range of cybersecurity experts and will be held at Cheltenham from 4 July to 9 September.
Another, named Cyber Exposure, is targeted at students with a "natural curiosity for technology and problem-solving".
The Cyber Exposure courses will be held at sites in Scarborough, the Manchester area, and the Thames Valley between 11 July and 19 August.
"It is good that GCHQ is doing this, it increases the number of people that are learning about cybersecurity," cryptography expert Prof Mark Ryan, at the University of Birmingham, told the BBC.
"We do have a cybersecurity skills gap where we just aren't training enough people in cybersecurity."
The Cheltenham-based school is targeted specifically at first- and second-year students studying computer science, maths, physics or related subjects.
The other courses are open to students of any subject who have five GCSEs, including maths and English, who are also on track to achieve two A-levels at C grade or higher.
In a statement, GCHQ said that work at the summer schools would cover a wide range of technologies.
"Students will learn about GCHQ's role in defending the UK against cyber-threats whilst being paid £250 a week," the agency said.
Applications are now open at the GCHQ careers website.

Ferdos Rabani, 48, currently at HMP Marshgate but formerly of Sheffield, was sentenced at the city's crown court.
Rabani, who is also known as Joshua Abdul, was found guilty of rape in November, said South Yorkshire Police.
In April 2016, he approached a 34-year-old woman, offered her a lift home before he drove to a remote area and raped her.
Rabani had offered her cigarettes, believed to have been drugged to make her drowsy, before the attack.
Several weeks afterwards the woman came forward to report to police what had happened.
PC Jess Hawley said: "Rabani could clearly see that the victim was vulnerable.
"He preyed on her and took advantage of her, leaving her incredibly traumatised by what happened."
UK intelligence agency GCHQ has announced it will pay £250 per week to students attending its Cyber Summer Schools this year.
[NEXT_CONCEPT]
A man who raped a "vulnerable" woman has been jailed for 24 years.