Aiming at the problem that training data is insufficient due to little training data in speaker recognition system, this paper adopts GMM-UBM as the background model which can identify the characteristics of the target speaker. And SVM is introduced to solve the problem of poor robustness of the system caused by GMM-UBM. It has much influence on SVM identification performance with different kernel functions. Aiming at the Characteristics of Polynomial kernel with good generalization ability and poor earning ability and Gaussian kernel with good earning ability and poor generalization ability, it structures a new combination kernel function which combines the advantages of each single kernel function by linear weighted method. The experimental results show that the recognition rate and Equal Error Rate of the combination kernel is more ideal than other kernel functions. And it achieves satisfactory recognition rate and robustness in the situations of different signal-to-noise ratio.