Sparse array is widely used in the field of array signal processing because of its advantages such as larger aperture and lower array mutual interference. The nested array and coprime array are sparse arrays which identify O(N2) sources, where N is the number of array elements. Many algorithms have recently been introduced to such identification. The method of high-order statistics can not only obtain better performance than the second-order moment, but also solve many problems that the second-order moment cannot solve. Moreover, the high-order statistics of additive white Gaussian noise is 0, which has the ability to suppress Gaussian white noise automatically. So in this paper, it is possible to combine higher-order statistics with MUSIC algorithm (HOS-MUSIC) on nested arrays and coprime arrays. Compared with direct MUSIC algorithm, HOS-MUSIC algorithm can also identify the two closely spaced sources without ambiguity in the two sparse arrays and the MSE of the HOS-MUSIC algorithm on sparse array is smaller. HOS-MUSIC algorithm will be demonstrated that there are more advantages in the sparse array DOA estimation. At the end of the paper, we also consider the use of nested arrays and coprime arrays for the case where the number of spaced sources is more than N.