Latin cubes are the high-dimensional form of Latin squares. Latin cubes have discreteness, uniformity and 3D attribute. There have been some applications of Latin squares in hash algorithms, but few applications of Latin cubes in this field. In this paper, a highly parallelizable hash algorithm based on four Latin cubes of order 4 is proposed. The parallelism is reflected in two aspects: on the one hand, the whole message is divided into several blocks, and all the blocks are processed in parallel; on the other hand, each block is further divided into several channels, and these channels are also processed in parallel. The whole hash procedure is based on four fixed Latin cubes. By the aid of uniformity and 3D attribute of Latin cubes, the algorithm has good statistical performances and strong collision resistance. Furthermore, the parallel structure makes the algorithm have satisfactory computation speed. Therefore the algorithm is quite suitable for the current applications of communication security.

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