In this paper, a space-time adaptive processing (STAP) method is proposed for the airborne radar with the array amplitude-phase error considered, which is based on atomic norm minimization (ANM). In the conventional ANM-based STAP method, the influence of the array amplitude-phase error is not considered and restrained, which inevitably causes performance deterioration. To solve this problem, the array amplitude-phase error is firstly estimated. Then, by pre-estimating the array amp-litude-phase error information, a modified ANM model is built, in which the array amplitude-phase error factor is separated from the clutter response and the clutter covariance matrix (CCM) to improve the estimation accuracy of the CCM. To prove that the atomic norm theory is applicable in the presence of the array amplitude-phase error, the clutter sparsity is analyzed in this pa-per. Meanwhile, simulation results demonstrate that the pro-posed method is superior to the state-of-the-art STAP method. Moreover, the measured data is used to verify the effectiveness of the proposed method.