To improve the precision of classification and recognition of transient power quality disturbances, a new classification and recognition algorithm for transient power quality disturbance signals, which is based on high-order cumulants (HOC) and support vector machine (SVM), is proposed. In the proposed algorithm, the 3-order and 4-order impulse statistical characteristics of two kinds of disturbances, i.e., the impulse transient and oscillation transient, are extracted from HOC, and eight characteristic quantities, i.e., the number of maximum values, the number of minimum values, the maximum and the minimum in 3-order and 4-order statistical results respectively, are chosen as the input of SVM. The proposed algorithm is verified by Matlab to obtain simulation data. Simulation results show that the transient disturbance characteristics can be effectively characterized by HOC and the disturbance characteristics are less influenced by noises; combining with SVM the two kinds of transient disturbances can be effectively recognized and identified. When training samples are 50 groups and the linear kernel function is chosen as the kernel function, the recognition rate can reach 99%; when other disturbance components are mixed with, the proposed algorithm is effective too.