Optimality conditions of approximate solutions for nonconvex semi-infinite multiobjective programming problem are established. By means of tangential subdifferential, some new regular conditions and generalized invex functions are defined. It’ s worth noting that the functions involved are not necessarily local Lipschitz. The definitions of (η,ε)-quasi weakly efficient solutions and (η,ε)-quasi efficient solutions for semi- infinite multiobjective programming problems are introduced. By the regular conditions, the necessary optimality condition of (η,ε)-quasi weakly efficient solutions is obtained. Moreover, the sufficient optimality condition of (η,ε)-quasi (weakly) efficient solutions is proposed by the generalized invex convexity. The results obtained in this paper improve and generalize the corresponding results in the literature.