M-estimation　is　a　widely　used　technique　for　robust　statistical　inference.　In　this　paper,　we　study　model　selection　and　model　averaging　for　M-estimation　to　simultaneously　improve　the　coverage　probability　of　confidence　intervals　of　the　parameters　of　interest　and　reduce　the　impact　of　heavy-tailed　errors　or　outliers　in　the　response.　Under　general　conditions,　we　develop　robust　versions　of　the　focused　information　criterion　and　a　frequentist　model　average　estimator　for　M-estimation,　and　we　examine　their　theoretical　properties.　In　addition,　we　carry　out　extensive　simulation　studies　as　well　as　two　real　examples　to　assess　the　performance　of　our　new　procedure,　and　find　that　the　proposed　method　produces　satisfactory　results.