The lack of stability is a problem encountered when applying the classical POD-Galerkin method to problems of unsteady compressible flows around a moving structure. To solve this problem, a hybrid reduced-order model named POD-ARX is constructed in this paper. The construction of this model involves two steps, including first extracting the fluid modes with the POD technique and then identifying the modal coefficients with the ARX model. The POD modes with the block of all modified primitive variables are extracted from the system response to the training signal. Once the POD modes are obtained, the snapshots are projected on these modes to determine the time history of modal coefficients and the resulting modal coefficients are used to identify the parameters of ARX model. Then, the ARX model is used to predict the modal coefficients of the system response to the validation signal. Sample two-dimensional aerodynamic force calculations are conducted to demonstrate this method. Results show that this method can produce a stable and accurate prediction to the aerodynamic response with significant improvement of computational efficiency for linear and even some nonlinear aerodynamic problems. In addition, this method also shows good wide-band characteristics by using the "3211" multistep signal as the training signal.