In order to reduce the time complexity of the kernel extreme learning machine,the L2.1-regularized kernel extreme learning machine based on the normal equation is proposed.The L2,1-norm is introduced into the objective function of the kernel extreme learning machine,and the opti-mal output weights of the L2.1-regularized kernel extreme learning machine are solved by using the normal equation,which effectively avoids the overfitting problem of the model,as well as improves the classification performance.Experiment results indicate that the proposed kernel extreme learn-ing machine can effectively decrease a large number of matrix operations in the learning process,and has faster learning speed as well as higher classification accuracy than the conventional kernel extreme learning machine.