A draft, submitted last week, sparked controversy over a clause that allows immunity for the generals who seized power in May last year.
Also causing concern is a clause which would allow unelected individuals to be appointed prime minister.
Thailand has seen almost a decade of divisive political conflict.
The previous constitution was abolished by the military after the coup. The current government operates under a temporary charter.
"We have drafted this constitution as it is a reform one, in hopes of leading the country out of cycles of conflicts, disunity and undemocratic fights," Gen Lertrat Ratanavanich, a spokesman for the Constitution Drafting Committee, told the AP news agency.
"I'm confident this constitution will provide justice to every side [of the conflict], more than the previous charters."
Under the new draft, future elections will be decided by a proportional representation system that leans towards smaller parties and coalition governments.
The upper house will mostly be unelected members; and the charter will allow parliament to choose as prime minister someone who is not a politician or an MP.
The BBC's Jonathan Head in Bangkok says the probable outcome of the new constitution will be weak and short-lived coalition governments, which would leave more power in the hands of the military and of senior, largely royalist bureaucrats, many of whom supported the coup.
The constitutional draft will be debated for six days, our correspondent adds, after which there will be very few opportunities for public discussion.
The military has ruled out a referendum but plans instead to seek opinion from a thousand selected respondents in each of Thailand's 77 provinces.
Critics say the constitution is aimed at preventing the return of former Prime Minister Thaksin Shinawatra.
He was ousted in 2006, after being accused of corruption and now lives in self-imposed exile.
Since then, Thailand has been deeply divided as his supporters and opponents struggle for political control, with the conflict sometimes spilling over into street violence.

De Villota lost her right eye at Duxford Airfield while testing for Marussia and died a year later aged 33.
The HSE said the driver's family had been informed of its decision.
Manor Grand Prix Racing, which operated Marussia and now runs the Manor team, has yet to comment.
De Villota, the daughter of 1980s F1 driver Emilio de Villota, was injured when the MR-01 race car she was driving hit a support truck on 3 July 2012.
She had been driving at up to 200mph (322km/h), but was travelling considerably slower at the time of the crash.
It was the first time the Spaniard had driven the car for Oxfordshire-based Marussia, which folded in 2014.
Despite losing her eye, she was cleared to drive again in early 2013, but died the following October "as a consequence of the neurological injuries she suffered".
Soon after the crash, Marussia said an internal investigation "excluded the car as a factor in the accident".
An HSE spokesman said: "The investigation is now complete and no enforcement action is being taken.
"Both the company [Manor Grand Prix Racing] and the DP's [deceased person's] family have been informed."
He said HSE had investigated "all reasonable lines of enquiry".
I was due to interview Maria and was standing with her mechanics when she came back in after a test run.
Her car slowed for it to be reversed into the pits, but at the last second it suddenly accelerated again.
By the time it hit the tailboard at the back of a truck, it was doing 30 or 40mph.
I could see the collision impacted directly on her helmet and I feared the worst.
It took almost an hour for ambulance staff to feel confident enough to take her out of the car.
It was an awful moment. I was surrounded by people who knew her very well, including family, friends, engineers and her manager.
Asked whether driver error had caused the crash, the spokesman said it was "not appropriate to disclose".
He added: "However, as with all accidents there are a number of underlying causes."
Speaking in October 2012 after leaving hospital, De Villota said: "I want to keep fighting because I believe so strongly in women being part of motor racing."
Thailand's military-picked reform council has begun a week-long debate over a new constitution, almost a year after a military coup.
[NEXT_CONCEPT]
No action is to be taken against a former Formula 1 team after test driver Maria de Villota suffered a severe crash in Cambridgeshire in 2012, the Health and Safety Executive (HSE) said.