In　this　paper,　we　propose　a　regularized　restricted　maximum　likelihood(REML)　method　for　simultaneous　variable　selection　in　heteroscedastic　regression　models.　Under　certain　regularity　conditions,　we　establish　the　consistency　and　asymptotic　normality　of　the　resulting　estimator.　A　simulation　study　is　conducted　to　illustrate　the　performance　of　the　proposed　method.