In　this　paper　we　are　concerned　with　the　problems　of　variable　selection　and　estimation　in　double　generalized　linear　models　in　which　both　the　mean　and　the　dispersion　are　allowed　to　depend　on　explanatory　variables.　We　propose　a　maximum　penalized　pseudo-likelihood　method　when　the　number　of　parameters　diverges　with　the　sample　size.　With　appropriate　selection　of　the　tuning　parameters,　the　consistency　of　the　variable　selection　procedure　and　asymptotic　properties　of　the　resulting　estimators　are　established.　We　also　carry　out　simulation　studies　and　a　real　data　analysis　to　assess　the　finite　sample　performance　of　the　proposed　variable　selection　procedure,　showing　that　the　proposed　variable　selection　method　works　satisfactorily.