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Latin hypercube sampling (LHS) method has difficulty in dealing with non-positive definite correlation matrices by traditional Cholesky decomposition, whereas it may often happen with the increasing scale of input variables. In order to improve the numerical stability of LHS, an improved LHS with modified alternating projections method (L-Mapm) is proposed in this paper. Compared with other two existing modified algorithms, L-Mapm is considered to possess accuracy, speediness, and controllability at the same time. The accuracy and effectiveness of L-Mapm applied to probabilistic load flow are proven by the comparative tests in the IEEE 33-bus system and PG&E 69-bus system. The simulation results show that L-Mapm has the best performance in modification and expands the application of LHS.