The support vector machine (SVM) is a classical machine learning method. Both the hinge loss and least absolute shrinkage and selection operator (LASSO) penalty are usually used in traditional SVMs. However, the hinge loss is not differentiable, and the LASSO penalty does not have the Oracle property. In this paper, the huberized loss is combined with non-convex penalties to obtain a model that has the advantages of both the computational simplicity and the Oracle property, contributing to higher accuracy than traditional SVMs. It is experimentally demonstrated that the two non-convex huberized-SVM methods, smoothly clipped absolute deviation huberized-SVM (SCAD-HSVM) and minimax concave penalty huberized-SVM (MCP-HSVM), outperform the traditional SVM method in terms of the prediction accuracy and classifier performance. They are also superior in terms of variable selection, especially when there is a high linear correlation between the variables. When they are applied to the prediction of listed companies, the variables that can affect and predict financial distress are accurately filtered out. Among all the indicators, the indicators per share have the greatest influence while those of solvency have the weakest influence. Listed companies can assess the financial situation with the indicators screened by our algorithm and make an early warning of their possible financial distress in advance with higher precision.