To improve the generalization performance of the sparse least square support vector machine for the high dimensional and heterogeneous data, a multi-kernel sparse least square support vector machine based on compressive sensing is presented. Firstly, according to the theory of compressive sensing, support vectors of the least square support vector machine are spared by the orthogonal matching pursuit algorithm. Then the new kernel matrix is calculated by the linear multi-kernel combination method. The solution of the sparse least square support vector machine is obtained by applying the new kernel matrix to the least square support vector machine. Finally, the function regression is achieved by using spares support vectors. The theoretical analyses and contract experiment results show the proposed algorithm has better performance and faster speed for high dimensional and heterogeneous data than those in the available, which greatly improves the generalization ability and operation speed of the algorithm.