In this paper, we consider variable selection for single-index models via martin- gale difference divergence. The important covariates are selected by maximizing penalized martingale difference divergence objective functions with fixed tuning parameters. To choose tuning parameters, we propose to use a BIC criterion. The consistency of the variable selection procedure with LASSO, SCAD and ALASSO penalties and asymptotic properties of the resulting estimators are established. The performance of the proposed procedure is assessed through extensive simulation studies. Finally, we apply the proposed method to real data sets.