This　paper　studies　the　least　squares　model　averaging　methods　for　two　non-nested　linear　models.　It　is　proved　that　the　Mallows　model　averaging　weight　of　the　true　model　is　root-n　consistent.　Then　the　authors　develop　a　penalized　Mallows　criterion　which　ensures　that　the　weight　of　the　true　model　equals　1　with　probability　tending　to　1　and　thus　the　averaging　estimator　is　asymptotically　normal.　If　neither　candidate　model　is　true,　the　penalized　Mallows　averaging　estimator　is　asymptotically　optimal.　Simulation　results　show　the　selection　consistency　of　the　penalized　Mallows　method　and　the　superiority　of　the　model　averaging　approach　compared　with　the　model　selection　estimation.