Quantum approximate optimization algorithm (QAOA) is a method for approximately solving combinatorial optimization problems, and has broad application prospects in related fields. It solves problems by repeatedly adjusting circuit parameters in order to maximize the expected value of Hamiltonian. In the research, QAOA is applied to the number partition problem (two partition problem). By converting the problem function into the corresponding Hamiltonian, a quantum circuit is constructed. The circuit parameters are optimized using constrained optimization by linear approximation (COBYLA) method, and the simulation experiment is carried out on IBMQ simulation platform. It is found that QAOA has good performance in number partition problems, which can obtain the solutions of the problems in polynomial time and reduce the time complexity of the problems.