Coal and gas outbursts are some of the most serious coal mine disasters, and effective prediction of coal and gas outbursts can reduce the likelihood of accidents and fatalities. Previously conducted studies have established that machine learning has achieved results in the prediction of coal and gas outbursts, but there is a problem that the available accident data of coal and gas outbursts are diminished or missing. This paper proposes a prediction model based on multiple filling of chained equations for random forests (miceforest) and the Harris Hawk optimization algorithm with Piecewise chaos mapping (PHHO) to optimize the kernel extreme learning machine (KELM) to solve the problem of missing data in coal and gas outburst prediction and to improve prediction accuracy in the case of missing data. Firstly, the miceforest algorithm was adopted to fill missing values in the salient samples, and then the PHHO algorithm was used to optimize the parameters of KELM. Finally, the datasets before and after filling were input into the PHHO−KELM model for experimentation and comparison with other models. The results show that miceforest filling is effective in improving the salient sample accuracy and overall accuracy of predictions, but the improvement is not significant for non-salient samples. The use of the PHHO−KELM model can effectively avoid falling into a local optimum and further improve the prediction accuracy of the KELM algorithm. The salient sample accuracy and overall accuracy of the miceforest−PHHO−KELM model prediction are 96.77% and 98.50%. And an effective coal and gas outburst model has been proposed, which is the miceforest−PHHO−KELM model.