The bag-of-visual-words (BOVW) and Fisher kernel are two popular models in human action recognition, and support vector machine (SVM) is the most commonly used classifier for the two models. We show two kinds of group structures in the feature representation constructed by BOVW and Fisher kernel, respectively, since the structural information of feature representation can be seen as a prior for the classifier and can improve the performance of the classifier, which has been verified in several areas. However, the standard SVM employs L2-norm regularization in its learning procedure, which penalizes each variable individually and cannot express the structural information of feature representation. We replace the L2-norm regularization with group lasso regularization in standard SVM, and a group lasso regularized-support vector machine (GLRSVM) is proposed. Then, we embed the group structural information of feature representation into GLRSVM. Finally, we introduce an algorithm to solve the optimization problem of GLRSVM by alternating directions method of multipliers. The experiments evaluated on KTH, YouTube, and Hollywood2 datasets show that our method achieves promising results and improves the state-of-the-art methods on KTH and YouTube datasets.