The harmonic balance method (HBM) is adapted in this paper to solve periodic unsteady flow problems. For these problems, this method has a high computational efficiency because it can rebuild the time history of a complete periodic flow with only computations at several equally spaced time intervals. The order of accuracy of the algorithm is guaranteed by employing a spectral operator to accurately solve the derivatives of the flow variables against the physical time. The mechanism and realization of the harmonic balance method are introduced in detail, and the process of modifying the existing code is presented. Two periodically forced pitching oscillation test cases are used to demonstrate the efficiency and accuracy of the harmonic balance method, including an airfoil in subsonic flow and a bluntcone configuration in hypersonic flow.A comparison is made with the dual time stepping method, and the results show that the harmonic balance method requires considerably more CPU memory, with the memory in N_H=2 case being four times that of the dual time-stepping method. Yet it can reduce the computing time greatly with only about 1/5 in N_H=2 case of that needed by the dual time-stepping method to obtain similar results. Therefore the harmonic balance method is an engineeringly applicable method with bright prospects. For problems with a long period, it has a more obvious advantage.