As a cutting-edge research direction in the field of radar imaging, video SAR has the capability of high-resolution and persistent imaging at any time and under any weather. Video SAR requires high computational efficiency of the imaging algorithm, and PFA has become the preferred imaging algorithm because of its applicability to the spotlight mode and relatively high computational efficiency. However, traditional PFA also has problems, such as low efficiency and limited scene size. To address the above problems, a generalized persistent polar format algorithm, called GPPFA, is proposed for airborne video SAR imaging that is applicable to the persistent imaging requirements of airborne video SAR under multitasking conditions. Firstly, the wavenumber domain resampling characteristics of video SAR PFA are analyzed, and a generalized resampling method is proposed to obtain higher efficiency. Secondly, for the problem of scene size limitation caused by wavefront curvature error, an efficient compensation method applicable to different scene sizes is proposed. GPPFA is capable of video SAR imaging at different wavebands, different slant ranges, and arbitrary scene sizes. Point target and extended target experiments verify the effectiveness and efficiency of the proposed method.