Many real-world optimization problems are challenging because the evaluation of solutions is computationally expensive. As a result, the number of function evaluations is limited. Surrogate-assisted evolutionary algorithms are promising approaches to tackle this kind of problems. However, their performance highly depends on the number of objectives. Thus, they may not be suitable for many-objective optimization. This paper proposes a novel hybrid algorithm for computationally expensive many-objective optimization, called C-M-EA. The proposed approach combines two surrogate-assisted evolutionary algorithms during the search process. We compare the performance of the proposed approach with seven multi-objective evolutionary algorithms. Our experimental results show that our approach is competitive for solving computationally expensive many-objective optimization problems.