Kernel function is the core of support vector machine (SVM) and directly affects the performance of SVM． In order to improve the learning ability and generalization ability of SVM for speech recognition，a Logistic kernel function，which is proved to be a Mercer kernel function，is presented． Experimental results on bi-spiral and speech recognition problems show that the presented Logistic kernel function is effective and performs better than linear，polynomial，radial basis and exponential radial basis kernel functions，especially in the case of speech rec-ognition．