<p>By considering predictors as nodes and their correlation as edges, a graphical structure can be imposed on predictors in a survival model. Some researchers have shown that by incorporating the graphical structure into regularized regression, the accuracy of variable selection and inference would increase. In this study, we present a double penalty in penalized likelihood function for the Cox proportional hazards model with a graphical structure among predictors. The proposed double penalty encourages sparsity not only among groups but also at individual levels. Theoretical properties such as the error bound and asymptotic distribution of the regularized estimators are investigated. Our simulation studies show that the proposed method outperforms the existing methods for the sparse Cox regression model with a graphical structure among predictors. The results of analyzing the progress of primary biliary cirrhosis (<b>PBC</b>) data also demonstrate the effectiveness of the proposed method.</p>