Least squares support vector machine (LS-SVM) has a large amount of computation and sparsity. Aiming at this problem, a fast sparse approximation least squares support vector machine (FSALS-SVM) algorithm is proposed. The algorithm uses an iterative algorithm of complexity to ac-celerate the calculation of the inverse of the kernel matrix and the sparse processing of the support vector machine through the pruning algorithm, thus reducing the computational complexity. The classification and recognition experiments of one dimension range profile of one dimensional radar target show that the FSALS-SVM is more sparsely under the same generalization performance.