This paper addresses the persistent imaging problem for a novel synthetic aperture radar (SAR) mode named curvilinear video SAR (CViSAR), involving the division of apertures and reconstruction of frame images. To form frame images with the same resolution, a new algorithm named adaptive aperture division (AAD) is proposed, which is based on the unification of effective spectrum supports (ESS). After that, the fast Gaussian grid non-uniform fast Fourier transform (FGG-NuFFT) is applied to form frame images in both high efficiency and high quality. Simulation experiment is provided to demonstrate the effectiveness.