The many-objective optimization performance of the Kriging-surrogate-based evolutionary algorithm (EA), which maximizes expected hypervolume improvement (EHVI) for updating the Kriging model, is investigated and compared with those using expected improvement (EI) and estimation (EST) updating criteria in this paper. Numerical experiments are conducted in 3-to 15-objective DTLZ1-7 problems. In the experiments, an exact hypervolume calculating algorithm is used for the problems with less than six objectives. On the other hand, an approximate hypervolume calculating algorithm based on Monte Carlo sampling is adopted for the problems with more objectives. The results indicate that, in the nonconstrained case, EHVI is a highly competitive updating criterion for the Kriging model and EA based many-objective optimization, especially when the test problem is complex and the number of objectives or design variables is large.