For short-term wind power forecasting, a KELM-AdaBoost method with weight update mechanism for a data set instance is proposed based on ensemble learning theory. The AdaBoost method can automatically learn multiple weak regressors and boost them into an arbitrarily accurate strong regressor, meanwhile, using kernel extreme learning machine (KELM) as the base learner of the AdaBoost method, which only adjusts the output weights of networks by using the regularization least square algorithm to achieve the minimum training error and the unknown nonlinear feature mapping of the hidden layer is represented with a kernel function, and the KELM method not only uses the RBF kernel function, but also uses the permissible multi-dimension tensor product wavelet kernel function. The proposed KELM-AdaBoost method is applied to the single-step direct forecasting of short-term wind power and the multi-step indirect forecasting in different regions respectively, and the validity of the KELM-AdaBoost method is verified by comparing its accuracy with RBF, SVM, ELM, KELM, RBF-AdaBoost, SVM-AdaBoost, ELM-AdaBoost methods under the same condition, the experiment results show that the proposed KELM-AdaBoost method is superior to the existing forecasting methods on the forecasting accuracy, therefore, it contains a huge potential and good application prospect.