Aiming at the nonsmooth DC optimization problem with convex inequality constraints,a double bundle method for convex constrained DC optimization problems based on penalty function is proposed. The dual problem of the double bundle method is also described. This method can effectively utilize the explicit convex DC decomposition structure of the nonconvex objective function. Firstly,the L1exact penalty technique is used to transform the convex constrained DC optimization problem into an unconstrained DC optimization problem,which is convenient for DC decomposition of the objective function directly. Then,the convex piecewise linear approximation model of the DC component of the augmented objective function is established,and finally the Lagrange function is used to obtain the equivalence relation between the optimal solution of the original problem and the optimal solution of the dual problem,which illustrates the feasibility and effectiveness of solving the search direction by using the dual problem.