There has been considerable interest in variable selection via regularization methods. However, most existing methods were developed for single index models in either parametric or semiparametric forms. Another line of statistical inquiry, sufficient dimension reduction, investigates the conditional independence between the response and predictors without assuming a specific model form. This motivates us to combine the merits of these two fields to develop a model-free variable selection method.  A regularized objective function is proposed for variable selection by utilizing a set of transformed responses as the multivariate pseudo-response. Subsequently, a hybrid of adaptive lasso (Zou, 2006) and group lasso (Yuan & Lin, 2006) is used to shrink coefficients. We refer to the proposed new approach as multivariate adaptive group lasso, and show that it selects significant variables consistently without imposing any restrictive model assumptions.