The comprehensive analysis of biological specimens brings about the demand for capturing the spatial, temporal and spectral dimensions of visual information together. However, such high-dimensional video acquisition faces major challenges in developing large data throughput and effective multiplexing techniques. Here, we report the snapshot hyperspectral volumetric microscopy that computationally reconstructs hyperspectral profiles for high-resolution volumes of ~1000 μm × 1000 μm × 500 μm at video rate by a novel four-dimensional (4D) deconvolution algorithm. We validated the proposed approach with both numerical simulations for quantitative evaluation and various real experimental results on the prototype system. Different applications such as biological component analysis in bright field and spectral unmixing of multiple fluorescence are demonstrated. The experiments on moving fluorescent beads and GFP labelled drosophila larvae indicate the great potential of our method for observing multiple fluorescent markers in dynamic specimens.