A backprojection algorithm (BPA), a time domain synthetic aperture radar (SAR) imaging algorithm, can be widely used without modification in various imaging modes, like stripmap, spotlight, sliding spotlight, etc. However, BPA also suffers when used in azimuth multichannel SAR due to the nonuniform sampling problem caused by a nonideal pulse repetition frequency. In this letter, we propose a weighted BPA (WBPA) for azimuth multichannel SAR imaging. Derived from the filter-bank-based reconstruction method, WBPA adds a weighting procedure to BPA. Simulations and an airborne SAR data experiment demonstrate that WBPA can perfectly suppress the azimuth ambiguities under band-limited circumstances. WBPA extends the applicable scope of BPA.