We　consider　model　averaging　estimation　problem　in　the　linear　regression　model　with　missing　response　data,　that　allows　for　model　misspecification.　Based　on　the　＇complete＇　data　set　for　the　response　variable　after　inverse　propensity　score　weighted　imputation,　we　construct　a　leave-one-out　cross-validation　criterion　for　allocating　model　weights,　where　the　propensity　score　model　is　estimated　by　the　covariate　balancing　propensity　score　method.　We　derive　some　theoretical　results　to　justify　the　proposed　strategy.　Firstly,　when　all　candidate　outcome　regression　models　are　misspecified,　our　procedures　are　proved　to　achieve　optimality　in　terms　of　asymptotically　minimizing　the　squared　loss.　Secondly,　when　the　true　outcome　regression　model　is　among　the　set　of　candidate　models,　the　resulting　model　averaging　estimators　of　the　regression　parameters　are　shown　to　be　root-n　consistent.　Simulation　studies　provide　evidence　of　the　superiority　of　our　methods　over　other　existing　model　averaging　methods,　even　when　the　propensity　score　model　is　misspecified.　As　an　illustration,　the　approach　is　further　applied　to　study　the　CD4　data.