Evolution strategy (ES) has shown to be effective in many search and optimization problems. In particular, the ES with covariance matrix adaptation (CMAES) achieves great successes and is viewed as a state-of-the-art evolutionary algorithm for complex numerical optimization. The CMAES models the population by a multivariate normal distribution, which requires a considerable amount of fitness evaluation results and thus degrades its efficiency. This paper proposes using fitness inheritance to reduce the computational cost at fitness evaluation. More specifically, the proposed FI-CMAES adopts fitness inheritance to approximate the fitness of offspring. The survivors are selected according to the approximated fitness; thereafter, the survival offspring are evaluated by the original fitness function. By this way, several original fitness evaluations on offspring can be saved. Experiments examine the effectiveness and efficiency of FI-CMAES on the CEC2014 test suite. The results show that FI-CMAES can outperform CMAES in terms of solution quality and convergence speed.