The accident happened shortly before 22:00 GMT on the New Lodge Road on Tuesday.
The man's condition was initially described as serious, but police have said he is now critical but stable in the Royal Victoria Hospital.
The New Lodge Road was closed for a time following the incident but has since re-opened.
Police have said they are following a number of lines of inquiry.
Det Insp Jenna Fitzpatrick said: "Information suggests that the car had been seen being driven dangerously in the area in the time leading up to the collision.
"The car was abandoned a short distance away from the scene at Donore Court."
Another car was struck by the green Ford Focus as it left the scene.

The 18-year-old man is still in hospital after the incident at Leicester's West Gate School on 27 January.
The school subsequently suspended three female members of staff.
Police confirmed the women were arrested in connection with allegations of neglect offences and then bailed pending further inquiries.
Chair of governors, the Rev Canon Peter Taylor, said: "A number of investigations are being carried out into the circumstances of this tragic incident.
"Three members of staff have been suspended while these take place."
A Leicestershire Police spokeswoman said the pupil "sustained injuries as a result of getting into difficulty in a swimming pool in Glenfield Road."
She added that the women "aged 49, 61 and 62, have been arrested in connection with the incident on neglect offences".
Leicester City Council and the Health and Safety Executive (HSE) are also investigating.
The school - which caters for students aged four to 19 with learning difficulties and disabilities - was officially opened by Prince Edward last year.

Cardiff-based SA Brain bought the chain Coffee #1 last year.
It comes as new figures show Brains' sales are up nearly 4% in its pubs.
Brains believes there is potential in the coffee market and plans a chain of about 50 outlets over the next three years in south Wales and the south west of England.
The family-run brewery employs about 2,000 people.
Last year's profits are up 6% against what the company described as "a tough economic backdrop".
In autumn 2011, Brains bought Coffee #1, which comprised 15 high street shops in south Wales and the south west of England, and since then, it has opened three more.
Brains chief executive Scott Waddington said: "The research suggests that the coffee market is going to continue to grow at 5, 6, 7% for the next five years, which is pretty much what it's been doing for the last five years.
"Coffee in the UK, despite more and more places opening, still has a long way to go to catch up with more developed markets, like the US."
Equity analyst Sam Hart said Brains' decision to diversify into coffee shops was "probably partly a reflection of very tough conditions in the on-trade [bar and pub sales] beer market".
"The on-trade is under pressure from a combination of pressure on consumers' disposable incomes, rising alcohol duties and the increased availability of relatively cheap beer at the supermarket chains," he added.
Mr Hart said the growth in the coffee shop culture in the UK could be viewed as Americanisation.
"Obviously coffee has been ingrained in culture in the US for many years and this appears to be spreading to the UK and other developed markets," he said.
"Many people view coffee as an affordable luxury on which they are prepared to spend, despite pressures on their disposable incomes."

The 22-year-old won the BBC's Women's Footballer of the Year Award in 2015 before joining Arsenal from Liverpool.
She helped the Gunners win the Women's FA Cup at Wembley in May 2016 and was recently awarded the African Women's Player of the Year Award.
She also played for her country at the 2015 Women's World Cup in Canada.
A man in his 30s who was hit by a car in north Belfast is in a critical condition in hospital.
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Three special school staff members were arrested after a teenage pupil was seriously injured in a swimming pool.
[NEXT_CONCEPT]
Wales' largest independent brewer is planning to open about 30 coffee shops over three years as it diversifies from its traditional pub business.
[NEXT_CONCEPT]
Nigeria winger Asisat Oshoala has left Women's Super League One club Arsenal Ladies to join Chinese side Dalian Quanjian.