Cameron Douglas, 31, pleaded guilty to the charges in January, following his arrest last year at the trendy Gansevoort Hotel in Manhattan.
In court, Douglas apologized to his family for "this nightmare of my own making" and admitted to a long heroin addiction.
"I believe, your Honor, that things will be difficult this time," Douglas told US District Judge Richard Berman.
His father, Michael Douglas, wrote a letter to the judge asking for leniency. He said Cameron had battled with drugs since age 13.
"I have some idea of the pressure of finding your own identity with a famous father," said Douglas, whose own father is actor Kirk Douglas. "I'm not sure I can comprehend it with two generations to deal with." In a separate letter, Michael Douglas' wife, actress Catherine Zeta-Jones, also wrote words of support.
"Never, in my experience over the years, has Cameron shown any signs of the disease, that has tormented him, toward his siblings, or has (he) ever been abusive to us as a family at any time," she wrote. "My stepson is a caring, considerate, worthy human being."
