Abstract: The uncertainty of transit travel times results in passengers' delay at the destination. Therefore it is necessary to take the risk awareness of passengers into account as one of the transit route choice standard. Firstly, the penalized cost of late arrival was incorporated in the transit route cost, which can describe passengers' route selection behavior. Then, transit equilibrium assignment model based on passengers' risk awareness was established. An algorithm based on route-specific costs was applied to the model and in a small transit network. The results indicated that passengers' route choice behavior can change from risk proneness to risk aversion as the increasing longest acceptable travel time, assuming the coefficient of late arrival penalized cost is larger than 1. So the penalized cost of late arrival can describe the risk awareness of passengers.