Summary: The bundle method shows very high efficiency in nonsmooth problems. For multiobjective convex programming problem, this paper attempts to find its weakly Pareto optimal solution with the aid of the bundle method. Firstly, an improved function is constructed by using the objective functions and the constraint functions. At the same time, the relationship between the improved function and the original problem is revealed. Then a lower approximation model of the improved function is constructed, and the next iteration point is generated by solving the quadratic programming subproblem. We use the Lagrange function to obtain the expression of optimal solution of the original subproblem.