In order to implement interactive and personalized Web services properly, it is necessary to understand the tangible and intangible responses of the users and to recognize their emotional states. Recently, some studies have attempted to build emotional state estimation models based on facial expressions. Most of these studies have applied multiple regression analysis (MRA), artificial neural network (ANN), and support vector regression (SVR) as the prediction algorithm, but the prediction accuracies have been relatively low. In order to improve the prediction performance of the emotion prediction model, we propose a novel SVR model that is optimized using a genetic algorithm (GA). Our proposed algorithm-GASVR-is designed to optimize the kernel parameters and the feature subsets of SVRs in order to predict the levels of two aspects-valence and arousal-of the emotions of the users. In order to validate the usefulness of GASVR, we collected a real-world data set of facial responses and emotional states via a survey. We applied GASVR and other algorithms including MRA, ANN, and conventional SVR to the data set. Finally, we found that GASVR outperformed all of the comparative algorithms in the prediction of the valence and arousal levels.