This study develops a data-driven group variable selection method for data envelopment analysis (DEA), a non-parametric linear programming approach to the estimation of production frontiers. The proposed method extends the group Lasso (least absolute shrinkage and selection operator) designed for variable selection on (often predefined) groups of variables in linear regression models to DEA models. In particular, a special constrained version of the group Lasso with the loss function suited for variable selection in DEA models is derived and solved by a new tailored algorithm based on the alternating direction method of multipliers (ADMM). This study further conducts a thorough evaluation of the proposed method against two widely used variable selection methods -- the efficiency contribution measure (ECM) method and the regression-based (RB) test -- in DEA via Monte Carlo simulations. The simulation results show that our method provides more favorable performance compared with its benchmarks.