In modern engineering design optimization problems, high-fidelity analyses are always used for evaluating objectives and constraints, which might be quite expensive. Thus, efficient global optimization method should be developed to relieve the computational burden. This paper proposed a dynamic surrogate-based optimization (DSBO) using Kriging model, of which two criteria for selecting infill samples in refinement procedure are employed: maximizing expected improvement (EI) function and minimizing surrogate prediction. The DSBO are validated to be robust and efficient by six standard analytical tests. The inequality constraints are handled by three different means here: constraining EI function, penalizing surrogate prediction, and penalizing objective function. Analytical tests and an engineering optimization problem with inequality constraints are carried out. The results indicate that simultaneous constraining EI function and penalizing surrogate prediction is most efficient for DSBO, and there is no need of adjusting penalty factor.