Many variations of Extreme Learning Machine （ELM） aim at improving the robustness of ELMs to outliers， while the traditional Robust Extreme Learning Machine （RELM） is very sensitive to outliers. How to deal with too many extreme outliers in the data becomes the most difficult problem for constructing RELM models. For outliers with large residuals， a bounded loss function was used to eliminate the pollution of outliers to the model； to solve the problem of excessive outliers， iterative modification technique was used to modify data to reduce the influence caused by excessive outliers. Combining these two approaches， an Iteratively Modified RELM （IMRELM） was proposed and it was solved by iteration. In each iteration， the samples were reweighted to reduce the influence of outliers and the under-fitting was avoided in the process of continuous modification. IMRELM， ELM， Weighted ELM （WELM）， Iteratively Re-Weighted ELM （IRWELM） and Iterative Reweighted Regularized ELM （IRRELM） were compared on synthetic datasets and real datasets with different outlier levels. On the synthetic dataset with 80% outliers， the Mean-Square Error （MSE） of IRRELM is 2.450 44， and the MSE of IMRELM is 0.000 79. Experimental results show that IMRELM has good prediction accuracy and robustness on data with excessive extreme outliers.