Shen Yongping's "A Hundred Years of Constitutionalism" is about the history of failed attempts to establish the rule of constitutional law in China, where the Communist Party has been in power since 1949.
DVDs were distributed for free and Shen had planned to post the documentary online as a free download, his lawyer Zhang Xuezhong told AFP.
"This charge is ridiculous, he didn't want to make any money from this film. If anything he lost money making it," Zhang said.
Shen's conviction comes less than a month after China celebrated its first national Constitution day and in the wake of a meeting of top Communist Party officials that decreed it is a "fundamental requirement" to ensure the rule of law.
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The country's constitution states: "Citizens of the People's Republic of China enjoy freedom of speech, of the press, of assembly, of association, of procession and of demonstration."
But the ruling party maintains a tight grip on expression, with protests regularly quashed and human rights lawyers and activists coming under increasing pressure since Xi Jinping took power two years ago.
The government harassed Shen throughout the filming process and repeatedly discouraged him from making the documentary, his lawyer said.
Shen has already been held for eight months, he added.