In the competitive electricity market, building optimal bidding strategies for generation companies (Gencos) could need to evaluate some market parameters such as rival's strategic bidding behavior, forecasting load and others. These parameters have the characteristic of uncertain variables in randomness and fuzziness. In the past work, due to the limit in mathematical theory, the model developed could not simultaneously consider these two kinds of uncertainties. Based on credibility theory accomplished recently, a new model with random fuzzy programming, which the two kinds of uncertainties of randomness and fuzziness are taken into account, is proposed in this paper for developing bidding strategies for Gencos with risk management, and a hybrid algorithm with integrating random simulation, artificial neural network and genetic algorithm is presented to solve the model. Finally, a numerical example of a simulated electricity market with six participating Gencos is presented for demonstrating the feasibility of the model and solution method.