Aiming at solving the Group Lasso of high-dimensional data or streaming data, the online learning model for the group lasso is proposed, and a closed-form solution of this model is obtained. Then the GFTPRL (Group Follow the Proximally Regularized Leader) algorithm is applied to logistic regression. Moreover, the GFTPRL algorithm's regret bound is proved to be good in online framework. Finally, the numerical results show that the prediction accuracy of the GFTPRL algorithm is significantly better than that of other mainstream sparse online algorithms when the sample size is large and the final model is sparse.