Accurately predicting and inferring a driver's decision to brake is critical for designing warning systems and avoiding collisions. In this paper we focus on predicting a driver's intent to brake in car-following scenarios from a perception-decision-action perspective according to his/her driving history. A learning-based inference method, using onboard data from CAN-Bus, radar and cameras as explanatory variables, is introduced to infer drivers' braking decisions by combining a Gaussian mixture model (GMM) with a hidden Markov model (HMM). The GMM is used to model stochastic relationships among variables, while the HMM is applied to infer drivers' braking actions based on the GMM. Real-case driving data from 49 drivers (more than three years' driving data per driver on average) have been collected from the University of Michigan Safety Pilot Model Deployment database. We compare the GMM-HMM method to a support vector machine (SVM) method and an SVM-Bayesian filtering method. The experimental results are evaluated by employing three performance metrics: accuracy, sensitivity, specificity. The comparison results show that the GMM-HMM obtains the best performance, with an accuracy of 90%, sensitivity of 84%, and specificity of 97%. Thus, we believe that this method has great potential for real-world active safety systems.