It investigates the algorithm for solving expensive many-objective black-box optimization problems. The algorithm ε-SOCEMO is proposed based on the SOCEMO algorithm, which uses ε-dominance for the target-value sampling strategy. Numerical experiments on algorithms ε-SOCEMO and SOCEMO were performed on 42 many-objective test problems, and the results show that ε-SOCEMO has better performance in the metrics. Numerical experiments show that this modified target-value sampling strategy can improve the computational effectiveness of the SOCEMO algorithm on expensive many-objective black-box optimization problems.