Snapshot channeled imaging spectropolarimetry (SCISP), which can achieve spectral and polarization imaging without scanning (a single exposure), is a promising optical technique. As Fourier transform is used to reconstruct information, SCISP has its inherent limitations such as channel crosstalk, resolution and accuracy drop, the complex phase calibration, et al. To overcome these drawbacks, a nonlinear technique based on neural networks (NNs) is introduced to replace the role of Fourier reconstruction. Herein, abundant spectral and polarization datasets were built through specially designed generators. The established NNs can effectively learn the forward conversion procedure through minimizing a loss function, subsequently enabling a stable output containing spectral, polarization, and spatial information. The utility and reliability of the proposed technique is confirmed by experiments, which are proved to maintain high spectral and polarization accuracy.