People often use finite mixing models to fit data with complex structures, but when faced with heavy tail data, the prediction accuracy is often inaccurate or the model component number is given incorrectly. In this paper, we design a semi-supervised mixture skew t distribution model for data with heavy tail structure, which can give ideal prediction accuracy for some data with labels and others without labels. Our model is more robust than the skew t distribution model, and we apply Monte Carlo sampling technique to the EM algorithm to solve the problem of expensive sampling. Finally, we give the simulation results. Compared with the skew t distribution model and the hybrid Gaussian model, our model has more robust fitting effect and smaller model prediction error.