The　lognormal　distribution　is　widely　used　in　applications.　Variable　selection　is　an　important　issue　in　all　regression　analysis　and　in　this　paper　we　investigate　simultaneous　variable　selection　in　the　joint　mean　and　dispersion　models　of　the　lognormal　distribution.　We　propose　a　unified　penalized　likelihood　method　which　can　simultaneously　select　significant　variables　in　the　mean　and　dispersion　models.　Furthermore,　the　proposed　variable　selection　method　can　simultaneously　perform　parameter　estimation　and　variable　selection　in　the　mean　and　dispersion　models.　With　appropriate　selection　of　the　tuning　parameters,　we　establish　the　consistency　and　the　oracle　property　of　the　regularized　estimators.　Some　simulation　studies　and　a　real　example　are　used　to　illustrate　the　proposed　method.