The　production　function　regression　models　with　time-varying　elasticity　coefficients　are　studied.　The　local　linear　weighted　least　squares　estimators　for　time-varying　elasticity　coefficient　functions　are　provided　by　the　local　polynomial　regression　method.　For　the　real　data　example　of　China,　the　time-varying　properties　of　the　elasticity　coefficients　are　studied.　By　the　generalized　likelihood　ratio　test,　the　capital　output　elasticity　and　the　labor　output　elasticity　in　China　are　not　constants　but　the　nonlinear　functions　of　the　time　in　the　period　of　1981-2004.　The　capital　output　elasticity　varies　from　0.21　to　0.68.　The　labor　output　elasticity　varies　from　0.44　to　0.89,　and　the　return　to　scale　varies　from　0.89　to　1.14.