Summary: In this article, we propose Bayesian penalized regression models for high-dimensional survival data. In the analysis of gene expression data, it is naturally assumed that genes are grouped according to some underlying process. Our proposed framework is motivated by the need of grouped shrinkage estimation to take such consideration into account. Special shrinkage priors are assigned on the regression parameters for the high-dimensional data where the dimension of the covariate space is much larger than the number of subjects. The priors correspond to the elastic net, group lasso, and fused lasso penalties which are popularly used to incorporate the grouping effect of the covariates in the analysis of microarray data. We adopted Bayesian Cox proportional hazards model where the cumulative baseline hazard function is modeled through a discrete gamma process prior. In the proposed Bayesian approach, the amount of grouped shrinkage are adaptively controlled by estimating tuning parameters via Markov chain Monte Carlo (MCMC) sampling method. The proposed methodologies are very useful when we want to incorporate the cluster structure of gene expression data into the models. We assess the prediction performance of our Bayesian penalized regression methods using simulations and real life high-dimensional survival data sets.