A linear compressor comprising: a cylinder that provides a compression space (P) for a refrigerant; a frame that fixes the cylinder to the interior of a shell ; a piston that reciprocates axially and is disposed inside the cylinder; a discharge valve that is disposed in front of the cylinder to selectively discharge the refrigerant compressed in the compression space; a discharge cover that is coupled to the frame, the discharge cover having a discharge space to receive the refrigerant discharged through the discharge valve; a valve spring that provides an axial resilient force to the discharge valve; and a valve support device to transfer vibration generated by the discharge valve to the frame, the valve support device being coupled to the valve spring and supported by the frame, the valve support device comprises: a support body that is disposed at one surface of the discharge cover and has a substantially ring shape; a cylinder support part that extends in a rearward direction from an outer peripheral surface of the support body and is supported by a surface of the cylinder ; wherein the cylinder support part comprises a first coupling part that receives a coupling member ; the linear compressor further comprises: a second coupling part that receives the coupling member and is formed in the cylinder ; and a third coupling part that is coupled with the coupling member and is formed in the frame ; wherein the coupling member passes through the first coupling part and the second coupling part to be coupled to the third coupling part . a cylinder that provides a compression space (P) for a refrigerant; a frame that fixes the cylinder to the interior of a shell ; a piston that reciprocates axially and is disposed inside the cylinder; a discharge valve that is disposed in front of the cylinder to selectively discharge the refrigerant compressed in the compression space; a discharge cover that is coupled to the frame, the discharge cover having a discharge space to receive the refrigerant discharged through the discharge valve; a valve spring that provides an axial resilient force to the discharge valve; and a valve support device to transfer vibration generated by the discharge valve to the frame, the valve support device being coupled to the valve spring and supported by the frame, the valve support device comprises: a support body that is disposed at one surface of the discharge cover and has a substantially ring shape; a cylinder support part that extends in a rearward direction from an outer peripheral surface of the support body and is supported by a surface of the cylinder ; wherein the cylinder support part comprises a first coupling part that receives a coupling member ; the linear compressor further comprises: a support body that is disposed at one surface of the discharge cover and has a substantially ring shape; a cylinder support part that extends in a rearward direction from an outer peripheral surface of the support body and is supported by a surface of the cylinder ; wherein the cylinder support part comprises a first coupling part that receives a coupling member ; the linear compressor further comprises: a second coupling part that receives the coupling member and is formed in the cylinder ; and a third coupling part that is coupled with the coupling member and is formed in the frame ; wherein the coupling member passes through the first coupling part and the second coupling part to be coupled to the third coupling part . <EOS>