Neutron coded imaging has been developed as a powerful tool to diagnose the two-dimensional (2-D) shape and size of a deuterium–tritium (DT) plasma in nuclear fusion. Compared with direct neutron radiography, it can extend the spatial resolution of the imaging system, whereas the image reconstruction process is necessary to deblur the coded image due to existence of the coded aperture. The Current reconstruction scheme is based on the linear imaging system, which requires the point spread function (PSF) at the center of field of view (FOV). However, there are three limitations with respect to imaging quality under this reconstruction scheme: one is the destruction of linear system as the coded aperture size increasing; one is the spatially translational variance of point spread function (PSF); another one is the system misalignment. Therefore, the coded aperture needs to be well designed to address those limitations. In this paper, we proposed a novel reconstruction scheme for neutron coded imaging with four-dimensional (4D) PSFs. Systematical comparisons of reconstructions with PSF at the center of FOV and 4D PSFs within FOV were performed. The results show reconstructions with 4D PSFs always achieve a similar accuracy no matter with the type and size of coded apertures, as well as precision of system alignment, whereas those with the PSF at the center of FOV show a different but lower accuracy. 4D PSFs are recommended to reconstruct the source image in neutron coded imaging.