Combining quantum approximate optimization algorithm to solve the constrained optimization problem is one of the current research hotspots. In order to solve the constrained optimization problem an improved method is proposed in the framework of the quantum approximate optimization algorithm. This method combines the quadratic unconstrained binary optimization method and the quantum alternate ansatz method adds penalty term to the target operator reduces the expected value of nonconforming solution and obtains feasible solution by solving the problem and limits the mixing operation to the feasible solution space and fuses together. The advantage of this method is that it can reduce the number of iterations and get the optimal solution quickly and accurately when solving constrained optimization problems. Taking the minimum vertex coverage problem as an example the proposed method is compared with several existing methods and it is concluded that the proposed method can reduce the number of iterations of the quantum approximate optimization algorithm so that the constrained optimization problem can be solved with high quality and high efficiency.