Jaycee Chan, who pleaded guilty to "hosting others to take drugs," was also fined 2,000 yuan ($320), announced the Dongcheng District People's Court.
Wearing a black sweatshirt and blue pants, the 32-year-old Chan -- who is an actor like his father -- bowed to the judge and prosecutor after the 90-minute trial.
"I committed a crime and deserve to be punished," the court's official microblog quoted him as saying. "It doesn't mean I have received mercy and forgiveness -- I hope to earn them with my future actions."
Reminding him to "return to the right path" and "establish a healthy public image," the prosecutor cited Chan's cooperation with police as a basis for leniency, according to the court.
The Hong Kong native
was arrested in Beijing last summer along with a Taiwanese actor, amid a government crackdown on celebrity drug offenders.
After both men tested positive for marijuana, police found more than 100 grams of the drug after searching Chan's apartment.
Although he did not attend the trial, Jackie Chan -- who has starred in Hollywood blockbusters like "Rush Hour" and was named an anti-drugs ambassador in China in 2009 -- had expressed anger and disappointment in his son in media interviews.
"I failed to discipline him -- now the state is helping me discipline him and make him get rid all the bad habits," the elder Chan, 60, told the state-run Xinhua news agency last month, while denying his son had received special treatment in jail.
The younger Chan's case has put a spotlight on the Chinese capital's intensifying anti-drugs campaign. By mid-November, the authorities had detained almost 10,000 people for using drugs, nearly double the previous year's figure.
Announcing the numbers, a top anti-narcotics official in Beijing emphasized the government's "zero-tolerance" stance on celebrity offenders due to the impact of their behavior on the youth.
Last August, dozens of management agencies representing actors and singers signed an agreement with Beijing authorities, banning drug use from the entertainment industry and pledging to fire any artists who break the law.