The　simultaneous　variable　selection　for　mean　model　and　variance　model　in　heteroscedastic　linear　models　is　discussed　in　this　paper.　We　propose　a　criterion　named　PIC　based　on　the　adjusted　profile　log-likelihood　function,　which　can　be　employed　to　jointly　select　regression　variables　in　the　mean　model　and　variance　model.　The　proposed　criterion　is　compared　with　the　naive　AIC　and　BIC　through　a　Monte　Carlo　simulation,　and　it　is　shown　that　PIC　outperforms　AIC,　and　is　comparable　with　BIC.　In　addition,　when　the　sample　size　is　not　large,　it　performs　the　best.