Mr. Bush, who served in the Texas Air National Guard, was more trusted by 69 percent while 24 percent said they trusted Kerry more, according to the National Annenberg Election Survey released Friday.
Among all Americans, Mr. Bush has a narrower advantage on trust to be commander in chief, 50-41.
The military sample was far more likely to be Republican than Democratic, which could help explain the more favorable view of the president. Four in 10, 43 percent, of the military sample said they were Republicans, while 19 percent said Democrats and 27 percent independents.
Those in the military and their families have a more favorable view of Mr. Bush than Americans generally, and they take a more optimistic view about Iraq, the economy and the nation's direction.
A majority in the military sample, 64 percent, said the country is on the right track. Among Americans generally, 55 percent said the country is headed in the wrong direction.
The National Annenberg Election Survey found that seven in 10, 69 percent, had a favorable view of Mr. Bush. Only three in 10, 29 percent, had a favorable view of Kerry.
The Annenberg poll, which does not report head-to-head preferences, did not ask the military respondents whom they support for president. The report cited a 1948 law that prohibits polling members of the military about their voting intent.
The poll of 655 in the active military and their families was taken Sept. 22-Oct. 5 and has a margin of sampling error of plus or minus 4 percentage points. Their answers were compared to those of 2,436 adults surveyed between Sept. 7-Oct. 3 with a margin of error of plus or minus 2 percentage points.