Concerning the classification problems of complex data distribution of scientific practice, economic life and many other fields, the correlation between variables could not be well described by using traditional Support Vector Machine (SVM), which would influence the classification performance. For this situation, Q-Gaussian function that was a parametric generalization of Gaussian function was put forward as the kernel function of SVM, and a financial early-warning model based on SVM with Q-Gaussian kernel was presented. Based on the financial data of A-share manufacturing listed companies of the Shanghai and Shenzhen stock markets, T-2 and T-3 financial early-warning model were constructed in experiments, the significance test was used to select some suitable indicators and the Cross Validation (CV) was used to determine model parameters. Compared to SVM model with Gaussian kernel, the forecasting accuracies of T-2 and T-3 model constructed by SVM with Q-Gaussian kernel were improved about 3%, and high-cost type I errors were reduced by at most 14.29%.