Defense lawyer Tran Thu Nam said the trial opened Tuesday in the central province of Nghe An amid tight security.
Nam said the defendants, 12 of them Catholics, are accused of working with the Viet Tan, or Vietnam Reform Party, in exile in the United States to carry out "activities aimed at overthrowing the people's administration." Four of them could face the death penalty if convicted.
The Vietnamese government has labeled Viet Tan as a terrorist group, but the U.S. government has said it has seen no evidence that the California-based group is a terrorist group.
Nam said the defendants, who were arrested in late 2011, are accused of attending Viet Tan's training overseas courses on nonviolent struggle and computer and Internet security. Some of them are also accused of participating anti-China protests and instigating others to join the protests.
People took to the streets in Hanoi for unprecedented weekly anti-China demonstrations in the summer of 2011 after Hanoi accused Beijing of interfering with its oil exploration activities in the South China Sea.
The verdicts are expected Wednesday.
International human rights groups have said Vietnam jails people for peacefully expressing their views, but Hanoi maintains that only lawbreakers are punished.