Nimoy died last month of complications of chronic obstructive pulmonary disease. He was 83.
The project is aimed at celebrating the 50th anniversary of TV series "Star Trek", which aired for the first time on September 8, 1966.
Zachary Quinto, who portrayed the Spock character in last two "Star Trek" films, will narrate the documentary.
David Zappone, the owner and president of Paramount-based 455 Films, will produce.
"This will be a tribute to my dad and Spock. We have plenty to work from because my dad loved telling stories and he was very fond of the role," Adam said.
The filmmaker said William Shatner, who played Enterprise captain James T Kirk, had agreed to appear in the documentary.
"My father wrote two books - 'I Am Not Spock' and 'I Am Spock' - and we've got lots of recordings so there's plenty for us to work with," he said.