Deep learning video compression outperforms its hand-craft counterparts with enhanced flexibility and capacity. One key component of the learned video codec is the autoregressive entropy model conditioned on spatial and temporal priors. Operating autoregressive on raster scanning order naively treats the context as unidirectional. This is neither efficient nor optimal, considering that conditional information probably locates at the end of the sequence. We thus introduce an entropy model based on a masked image modeling transformer (MIMT) to learn the spatial-temporal dependencies. Video frames are first encoded into sequences of tokens and then processed with the transformer encoder as priors. The transformer decoder learns the probability mass functions (PMFs) \emph{conditioned} on the priors and masked inputs. Then it is capable of selecting optimal decoding orders without a fixed direction. During training, MIMT aims to predict the PMFs of randomly masked tokens by attending to tokens in all directions. This allows MIMT to capture the temporal dependencies from encoded priors and the spatial dependencies from the unmasked tokens, i.e., decoded tokens. At inference time, the model begins with generating PMFs of all masked tokens in parallel and then decodes the frame iteratively from the previously-selected decoded tokens (i.e., with high confidence). In addition, we improve the overall performance with more techniques, e.g., manifold conditional priors accumulating a long range of information, shifted window attention to reduce complexity. Extensive experiments demonstrate the proposed MIMT framework equipped with the new transformer entropy model achieves state-of-the-art performance on HEVC, UVG, and MCL-JCV datasets, generally outperforming the VVC in terms of PSNR and SSIM.