Along a roughly chronological order, the azimuth signals undersampled from the multichannel synthetic aperture radar (SAR) for high-resolution wide-swath (HRWS) imaging correspond to recurrent nonuniform sampling. Only a finite-duration sequence of samples of the azimuth signal can be obtained in practical applications. A new recurrent nonuniform sampling scheme can be generated by extending these samples periodically across the boundaries provided that the azimuth signal is bandlimited. Thus, from the perspective of reconstructing recurrent nonuniform sampling, an innovative reconstruction algorithm for suppressing azimuth ambiguities of multichannel HRWS SAR is proposed, which is suitable to be implemented on digital computers. Furthermore, the presented algorithm acquires the filter weights without matrix inversion reducing tremendously the computational load.