<p>In this study, we consider the optimization problem of continuous-time Markov decision processes with a metric combining the mean and variance of the long-run average reward. Besides the mean reward, its variance is also significant, which can reflect the risk and fluctuation of the system and characterize the optimization problem more sufficiently. However, the variance term is a quadratic form, and it can be affected by action selections of both current and future stages. Therefore, traditional approaches such as establishing the optimality equation and dynamic programming are not feasible here because of the time inconsistency. We study this problem with a method called sensitivity-based optimization theory. We can obtain a performance difference formula that compares the difference between two policies by utilizing this theory. Based on this formula, we give a necessary condition for optimal policies and prove the existence of a deterministic stationary optimal policy in the randomized stationary policy space. Moreover, the performance difference formula can be utilized to develop a policy iterative algorithm and prove that it converges to a local optimum. Finally, we prove the feasibility of using the trust region method to solve the optimization problem and give a new algorithm based on it.</p>