The adaptive angle-Doppler compensation method adaptively extracts requisite information based on the data itself, thereby avoiding the problem of performance degradation due to inertial system error. However, this method requires the estimation and eigen decomposition of a sample covariance matrix, which has high computational complexity and limits its real-time application. In this paper, we investigate an adaptive angle-Doppler compensation method based on Projection Approximation Subspace Tracking (PAST). This method uses cyclic iterative processing to quickly estimate the positions of the spectral center of the maximum eigenvector in each range cell, thereby avoiding the computational burden of matrix estimation and eigen decompositon. Then, the spectral centers of all range cells are overlapped by two-dimensional compensation. Our simulation results demonstrate that the proposed method can effectively reduce the nonhomogeneity of airborne bistatic radar, with a performance is similar to that of eigen-decomposition algorithms, but with a reduced computational load and easy implementation.