Chan, whose son was jailed for drugs offences, said that with drugs "you're hurting thousands of young children".
Jaycee Chan spent six months in prison in China after police found marijuana in his home.
Jackie Chan is Singapore's first celebrity anti-drug ambassador. He was named official Narcotics Control Ambassador by Chinese police in 2009.
Both Singapore and China have enforced capital punishment for drug trafficking.
In an interview with journalists conducted in both English and Mandarin, he said drugs were not only hurting young people, they were hurting his family.
"On some issues, I do support the death penalty," he said.
"When you're hurting thousands and thousands of young children, I think these kind of people are useless.
"You should get the right punishment."
He added: "[Young people say] 'it's okay, it's just like a cigarette'. I say 'it's not okay, not in my family'."
Jaycee, 32, was imprisoned for not just using drugs, but for the additional and more serious crime of "providing a shelter for others to abuse drugs", Beijing police said at the time.
When asked about Jaycee's time in prison, Chan said he felt "ashamed" and "shocked" and that he was now more focused on his son.
"I'm more concentrating on him now, used to be just, 'you are a grown man.' But now I find out, he's still a boy," Chan said.
Hong Kong actor Jackie Chan has said he supports the use of the death penalty for some drug offenders.