Statical causal discovery is an approach to infer the causal relationship between observed variables whose causalities are not revealed. LiNGAM (Linear Non-Gaussian Acyclic Model), an algorithm for causal discovery, can calculate the causal relationship uniquely if the independent components of variables are assumed to be non-Gaussian. However, use-cases of LiNGAM are limited because of its O(d3x) computational complexity, where dx is the number of variables. This paper shows two approaches to accelerate LiNGAM causal discovery: SIMD utilization for LiNGAM's mathematical matrixes operations and MPI parallelization. We evaluate the implementation with the supercomputer Fugaku. Using 96 nodes of Fugaku, our improved version can achieve 17,531 times faster than the original OSS implementation (completed in 17.7 hours).