A spectrum reconstruction algorithm based on space–time adaptive processing (STAP) can effectively suppress azimuth ambiguity for multichannel synthetic aperture radar (SAR) systems in azimuth. However, the traditional STAP-based reconstruction approach has to estimate the covariance matrix and calculate matrix inversion (MI) for each Doppler frequency bin, which will result in a very large computational load. In addition, the traditional STAP-based approach has to know the exact platform velocity, pulse repetition frequency, and array configuration. Errors involving these parameters will significantly degrade the performance of ambiguity suppression. A modified STAP-based approach to solve these problems is presented. The traditional array steering vectors and corresponding covariance matrices are Doppler-variant in the range-Doppler domain. After preprocessing by a proposed phase compensation method, they would be independent of Doppler bins. Therefore, the modified STAP-based approach needs to estimate the covariance matrix and calculate MI only once. The computation load could be greatly reduced. Moreover, by combining the reconstruction method and a proposed adaptive parameter estimation method, the modified method is able to successfully achieve multichannel SAR signal reconstruction and suppress azimuth ambiguity without knowing the above parameters. Theoretical analysis and experiments showed the simplicity and efficiency of the proposed methods.