Focusing on the issue that the method of Back Propagation (BP) neural network limits the prediction accuracy of the short term electricity load, a prediction model based on Extreme Learning Machine with Kernels and Iterative Error Correction (KELM-IEC) was proposed. Firstly, an input index system was built, in which 7 factors were selected as the input of the prediction model, namely, month of the year, day of the month, day of the week, week number, holiday, daily average temperature, and maximum electricity load for the day before. Secondly, a load prediction model was built. It was based on a new kind of neural network called Extreme Learning Machine with Kernels (KELM). KELM introduced the kernel function mapping of Support Vector Machine (SVM) as the hidden layer nodes mapping of Extreme Learning Machine (ELM). It combined the advantages of ELM with simple structure and SVM with good generalization ability effectively, which could improve the prediction accuracy. Finally, an Iterative Error Correction (IEC) model was built based on the method of IEC in the field of time series prediction. The prediction errors of the load prediction model were trained by KELM and the prediction results could be corrected and revised. Thus, the prediction errors could be decreased and the predictive performance could be improved. In simulation experiments of two actual electricity load data sets, the KELM-IEC model was compared with the BP neural network model, and Mean Absolute Percentage Error (MAPE) respectively decreased by 74.39% and 34.73%, while Maximum Error (ME) decreased by 58.34% and 39.58%, respectively. At the same time, the KELM-IEC model was compared with the KELM model, and MAPE decreased by 18.60% and 4.29% respectively, while ME decreased by 0.08% and 11.21%, respectively, which verified the necessity of the IEC strategy. The simulation experiment results show that the KELM-IEC model can improve the prediction accuracy of the short term electricity load. It can benefit the plan, operation and management of the power system. It can guarantee the demand for production and living electricity. And it can improve both the economic and social benefits.