At least 6,256 US veterans committed suicide in 2005 -- an average of 17 a day -- the network reported, with veterans overall more than twice as likely to take their own lives as the rest of the general population.
While the suicide rate among the general population was 8.9 per 100,000, the level among veterans was between 18.7 and 20.8 per 100,000.
That figure rose to 22.9 to 31.9 suicides per 100,000 among veterans aged 20 to 24 -- almost four times the non-veteran average for the age group.
"Those numbers clearly show an epidemic of mental health problems," CBS quoted veterans' rights advocate Paul Sullivan as saying.
CBS quoted the father of a 23-year-old soldier who shot himself in 2005 as saying the military did not want the true scale of the problem to be known.
"Nobody wants to tally it up in the form of a government total," Mike Bowman said. "They don't want the true numbers of casualties to really be known."
There are 25 million veterans in the United States, 1.6 million of whom served in Afghanistan and Iraq, according to CBS.
"Not everyone comes home from the war wounded, but the bottom line is nobody comes home unchanged," Paul Rieckhoff, a former Marine and founder of Iraq and Afghanistan Veterans for America told the network.
CBS said it was the first time that a nationwide count of veteran suicides had been conducted. The tally was reached by collating suicide data from individual states for both veterans and the general population from 1995.
The Department of Veterans Affairs spends some three billion dollars a year on mental health services, according to CBS.