With the ever-increasing number of vehicles on the road, traffic accidents have also increased, resulting in the loss of lives and properties, as well as immeasurable social costs. The environment, time, and region influence the occurrence of traffic accidents. The life and property loss is expected to be reduced by improving traffic engineering, education, and administration of law and advocacy. This study observed 2,471 traffic accidents which occurred in central Taiwan from January to December 2011 and used the Recursive Feature Elimination (RFE) of Feature Selection to screen the important factors affecting traffic accidents. It then established models to analyze traffic accidents with various methods, such as Fuzzy Robust Principal Component Analysis (FRPCA), Backpropagation Neural Network (BPNN), and Logistic Regression (LR). The proposed model aims to probe into the environments of traffic accidents, as well as the relationships between the variables of road designs, rule-violation items, and accident types. The results showed that the accuracy rate of classifiers FRPCA-BPNN (85.89%) and FRPCA-LR (85.14%) combined with FRPCA is higher than that of BPNN (84.37%) and LR (85.06%) by 1.52% and 0.08%, respectively. Moreover, the performance of FRPCA-BPNN and FRPCA-LR combined with FRPCA in classification prediction is better than that of BPNN and LR.