A variable valve apparatus includes a high lift cam and a low lift cam in parallel with the high lift cam. A tappet body includes a high lift tappet body that constantly contacts the high lift cam, and a low lift tappet body that is disposed in the high lift tappet body and selectively contacts the low lift cam. An inner column is connected with a valve and reciprocally disposed within the low lift tappet body. A supporting member is disposed below the tappet body. A lost motion elastic member is disposed between the supporting member and the tappet body for supplying restoring force to the tappet body. A first connector selectively connects the high lift tappet body and the low lift tappet body. A second connector selectively connects the low lift tappet body and the inner column.