Carbon price and electricity price are bound together under the influence of external factors. Thus, the price randomness of carbon and electricity along with their correlation should be taken into consideration to form the bidding model for generation companies. The difference between actual profit and the expectation is defined as the risk and measured by multi-stochastic conditional risk method in this paper. Then, a CVaR-based bidding model which considers the price randomness of electricity and carbon along with their correlation is proposed. The Linear method is used to sample of the random variables concerning the correlation and to solve the conditional value at risk. Cases considering the correlation between electricity price and carbon price, carbon price cost, carbon price randomness and other risk measurement methods are tested respectively to evaluate their influences on the investment decision risk of generation companies. The results show that considering the price randomness of both electricity and carbon as well as their correlation is more in accordance with the generation companies’ requirement of increasing revenue and reducing risk, and conditional risk method is able to describe the risk more accurately.