An adaptive and iterative LSSVR algorithm based on quadratic Renyi entropy is presented in this paper. LS-SVM loses the sparseness of support vector which is one of the important advantages of conventional SVM. The proposed algorithm overcomes this drawback. The quadratic Renyi entropy is the evaluating criterion for working set selection, and the size of working set is determined at the process of iteration adaptively. The regression parameters are calculated by incremental learning and the calculation of inversing a large scale matrix is avoided. So the running speed is improved. This algorithm reserves well the sparseness of support vector and improves the learning speed.