A spokesman for Kalanick said the lawsuit is "completely without merit and riddled with lies and false allegations."
In the lawsuit, Benchmark claims Kalanick concealed material information from investors when he created three new board seats in 2016 and gave himself the right to appoint people to those seats.
Among other things, Benchmark said, Kalanick knew Uber might be accused of stealing trade secrets from Waymo, Google's self-driving car unit.
Waymo sued Uber earlier this year. The lawsuit also says Kalanick didn't discuss his failure to curb Uber's pervasive culture of discrimination and sexual harassment.
Kalanick resigned under pressure in June after a monthslong investigation into harassment and other behaviour problems at the San Francisco-based company.
But he quickly appointed himself to one of the three board seats. The other two remain vacant.
Benchmark says Kalanick has acquired "a disproportionate level of influence over the board, ensuring that he would continue to have an outsized role in Uber's strategic direction even if forced to resign as CEO."
The firm says Kalanick has already interfered in the board's attempts to hire a new chief executive.
Benchmark wants to remove the three additional seats and return the board to eight members.
It's also asking the court to prevent Kalanick from participating in board meetings.
Uber said it had no comment on the lawsuit. But in a statement, Kalanick's spokesman said the lawsuit is an attempt to deprive Kalanick of his rights as an Uber founder and shareholder.
"Travis will continue to act in the interests of Uber and all of its stakeholders and is confident that these entirely baseless claims will be rejected," the statement said.