The existences of solutions to the generalized second-order invex vector variational-like inequality are investigated, and their relationships with those of multi-objective optimization problems are disclosed. Two classes of generalized second-order invex functions and a type of second-order monotone functions are introduced, some specific examples are presented to illustrate their existences. The relationships with respect to the solutions between vector variational-like inequalities and multi-objective optimization problems are established by using analytical method. Based on KKM theorem, the existence results of vector variational-like inequalities are obtained under the assumptions of the introduced second-order monotonicity. It is shown that the solutions of vector variational-like inequalities are existed and it exists the closely relationships with multi-objective optimization problems under the appropriate conditions.