Toyoda, the grandson of the company's founder and previously its chief executive, last year was re-elected to the board with around 85% approval, a drop from the previous year's almost 96%.
That represented a rare rebuke in corporate Japan where board members are frequently re-elected with near unanimous shareholder endorsement.
Last year, too, Glass Lewis recommended a vote against Toyoda, citing what it said was his responsibility for a lack of board independence.
No one was immediately available to comment on the matter at Toyota.
The automaker has previously said its board meets governance standards set by the Tokyo Stock Exchange.
Last year it said Toyoda had been re-nominated because he would push transformation of the company. Glass Lewis also said shareholders should vote against re-electing the board's vice chairman, Shigeru Hayakawa, showed a copy of its recommendations to shareholders shared with Reuters on Tuesday. It did not recommend such last year.
It said shareholders should also vote against a proposal urging the manufacturer to align its lobbying activity with the Paris Agreement on climate change.
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