Metasurface-assisted computational imaging has emerged as a promising route for complex optical field reconstruction. Multi-channel lensless imaging has been proved by leveraging the diverse ingredients of the optical field that can be deliberately manipulated by flat-optics. However, achieving single-shot multi-channel images by a single-cell metasurface is challenging due to the apparent capacity limitation of a single kind of meta-atom. In this work, we introduce an end-to-end inverse design method based on gradient-descent optimization algorithm for multi-channel lensless computational imaging, realizable by a single-cell metasurface. The proposed method directly provides single-cell metasurfaces without the need of complex meta-atom design strategy, which offers high efficiency and eases the fabrication. Particularly, multi-spectral, multi-depth (3D) and polarimetric imaging is demonstrated by a phase-only metasurface across the visible and near-infrared band. Our results prove a viable scheme towards practical metasurface generated lensless image reconstruction, by demonstrating the high-density information coding of single-cell metasurface. The scheme is expected to enable optical storage, optical encryption, holographic display, and full-color and three-dimensional imaging applications.