In order to solve small sample and overfitting problems as well as improve recognition performances, palmprint recognition is studied based on support vector machine (SVM). The kernel function is used to map nonlinear sample space onto another high dimension linear space. For this purpose, a new kernel function is proposed. The function consists of radial basis of functions(RBF) and polynomials, so it is a kind of combination kernel function. In the preprocessing of palmprint image, palm region of interest is cut by using the largest inscribed circle approach. Then the “eigenpalms” are extracted by means of principal component analysis. At the stage of recognition, support vector machine is used as a classified tool. An efficient algorithm is given about how to find proper weight parameters and kernel parameters for obtaining good classified performances. Consequently the accuracy of palmprint recognition can be increased. Experiments show that the method can solve sample training problems well and support vector machine of combination kernel function shows better generalization performance than that of the single kernel function.