Fifty-five percent of those questioned nationally said marijuana should be made legal, with 44% disagreeing.
The CNN/ORC findings are similar to a Gallup poll conducted in October.
According to the CNN poll and numbers from General Social Survey polling, support for legalizing marijuana has steadily soared over the past quarter century - from 16% in 1987 to 26% in 1996, 34% in 2002, and 43% two years ago.
The survey found interesting divides on the issue.
"There are big differences on age, region, party ID, and gender, with senior citizens, Republicans, and Southerners the only major demographic groups who still oppose the legal use of pot," said CNN Polling Director Keating Holland.
Two-thirds of those 18 to 34 said marijuana should be legal, with 64% of those 34 to 49 in agreement.
Half of those 50 to 64 believe marijuana should be legal, but that number dropped to 39% for those age 65 and older.
Support stood at 60% in the Northeast, 58% in the West, 57% in the Midwest, but just 48% in the South. Sixty-two percent of Democrats and 59% of Independents, but just 36% of Republicans, backed legalizing marijuana. Fifty-nine percent of men but just 51% of women supported making pot legal.
Attitudes have dramatically changed
Why has support for legalizing marijuana tripled since the 1970s and 1980s?
"Attitudes toward the effects of marijuana and whether it is morally wrong to smoke pot have changed dramatically over time," said Holland. "That also means that marijuana use is just not all that important to Americans any longer."
In 1972, about a year after President Richard Nixon declared drugs "public enemy Number One," 65% said the use of marijuana was a very serious problem for the United States. Now that is down to 19%.
The number who said marijuana is a gateway drug (47%), is down 23 points since 1972. The number who said marijuana is addictive (50%), is down 10 points. And the number who said marijuana is physically harmful (43%) is down 23 points.
"Clearly there are some reservations about marijuana, but not the widespread fear that existed during the original War on Drugs in the 1970s," added Holland.
The biggest change indicated by the poll reflected the number of people who said smoking pot is morally wrong. In 1987, 70% said it was, making it a sin in the minds of more Americans than abortion or pornography.
Now, that number has been halved - just 35% today said smoking marijuana is morally wrong.
Widespread agreement that it is not morally wrong may be one of the bigger drivers of the pro-legalization movement.
The CNN poll was conducted by ORC International, from January 3-5, with 1,010 adults nationwide questioned by telephone. The survey's overall sampling error is plus or minus 3 percentage points.
CNN Political Editor Paul Steinhauser contributed to this report
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