A convex upper approximation method for non-convex multi-objective optimization problems is presented. First, the multi-objective optimization problem is transformed into a single-objective optimization problem using the ε-constraint method. Second, a class of convex upper estimation function is used to approximate the non-convex constraint function, and a series of convex relaxation subproblems are constructed. A sequential parametric convex approximation algorithm is designed. Third, under appropriate conditions, it is proven that the iterative sequence generated by the algorithm converges to the KKT point of the original multi-objective optimization problem. Finally, numerical experiments are conducted to verify the feasibility of the algorithm.