A　regression　model　with　skew-normal　errors　provides　a　useful　extension　for　ordinary　normal　regression　models　when　the　data　set　under　consideration　involves　asymmetric　outcomes.　Variable　selection　is　an　important　issue　in　all　regression　analyses,　and　in　this　paper,　we　investigate　the　simultaneously　variable　selection　in　joint　location　and　scale　models　of　the　skew-normal　distribution.　We　propose　a　unified　penalized　likelihood　method　which　can　simultaneously　select　significant　variables　in　the　location　and　scale　models.　Furthermore,　the　proposed　variable　selection　method　can　simultaneously　perform　parameter　estimation　and　variable　selection　in　the　location　and　scale　models.　With　appropriate　selection　of　the　tuning　parameters,　we　establish　the　consistency　and　the　oracle　property　of　the　regularized　estimators.　Simulation　studies　and　a　real　example　are　used　to　illustrate　the　proposed　methodologies.