In the restructured electricity market, retailers are intermediaries between the electricity wholesale market and consumers. Considering the uncertainty of wholesale market price, retailers should consider the risks of their profit caused by the uncertain wholesale price when participating in the retail competition. Indeed, retailers’ risk preferences will impact their price bidding strategies. To examine the effects of retailers’ risk preferences on their strategies and equilibrium outcomes in the retail market, an equilibrium model for price-making retailers is proposed by employing the mean−variance utility theory to model the risk preferences of retailers. The market share function is used to characterize consumers’ price-elasticity and switching behavior in the retail market. Few works in the literature address the issue of bidding strategies of retailers with different risk preferences in the electricity market with switchable consumers. Moreover, the existence and uniqueness of the Nash equilibrium are theoretically proved. A theoretical analysis is presented to investigate the impacts of wholesale price uncertainty and retailer’s risk preference on the bidding strategy. By adopting the nonlinear complementarity approach, the proposed game model is transformed into a set of nonlinear equations, which is further solved by the Levenberg−Marquardt algorithm. Finally, examples are included to verify the effectiveness of the proposed theory, and the results show that the bidding price of a retailer will increase with the increasing uncertainty of the wholesale price and the increasing risk-averse levels of itself and its rivals.