We develop a novel Bayesian doubly adaptive elastic-net Lasso (DAELasso) approach for VAR shrinkage. DAELasso achieves data selection and coecients shrinkage in a data based manner. It constructively deals with the explanatory variables that tend to be highly collinear by encouraging grouping eect. In addition, it allows for different degree of shrinkages for dierent coecients. Rewriting the multivariate Laplace distribution as a scale mixture, we establish closedform posteriors that can be drawn from a Gibbs sampler. We compare the forecasting performance of DAELasso to that of other popular Bayesian methods using US macro economic data. The results suggest that DAELasso is a useful complement to the available Baysian VAR shrinkage methods.