Abstract: Considering the neglect of kernel function cost and lack of sparsity of multiple kernel least squares support vector machine (MK-LSSVM), a cost-constraint based multiple kernel least squares vector machine with sparsity is proposed. The primal optimal problem of MK-LSSVM is converted into second-order cone programming, and then the weight of complex kernel function is restricted by introducing cost factors so as to save storage space and computing time of variable quantity. Furthermore, the kernel matrices are reduced by Schmidt orthogonalization theory to lower computational complexity. The total cost of multiple kernel learning can be evaluated according to the number of support vectors and active kernel functions. The simulation results on testing datasets show that the proposed method can achieve the same accuracy as MK-LSSVM by using less support vectors and simpler mixture kernel functions with cheaper consumption and better real-time performance. The cost vaule of froth flotation mineral recovery prediction used the proposed method reduces 27.56.