Three voters want the Supreme Court to stop IEBC from conducting the repeat election on Thursday.
They say the electoral agency is unprepared and threats to its employees may prejudice the outcome of the election.
Khalef Khalia, Samuel Monochi and Gacheke Gachini have named IEBC chair Wafula Chebukati as a respondent.
They claim there is an active plan to sabotage and frustrate the fresh election so IEBC cannot conduct a free, fair and credible process.
The voters argue that although logistical and operational arrangements have been made, the political environment and Kenyans' confidence is key.
They further claim the withdrawal of NASA leader Raila Odinga and his running mate Kalonzo Musyoka triggered a vacation of the repeat election.
Raila has clarified his instructions for voting day, saying his supporters should stay away, not demonstrate, in their push for reforms at IEBC.
The Opposition leader had said mega demonstrations would take place across the country on Thursday.
"We have not told people to demonstrate on the polling day. We have not said that at all. We have told people to stay away," Raila told BBC.