A muffler for a compressor and a compressor having the same are provided, in which a suction noise device and a discharge noise device may be integrally formed to reduce a number of components of a suction side muffler and a discharge side muffler so as to reduce leakage of refrigerant generated at an assembled portion of the muffler, and to reduce a length of a suction passage and a discharge passage. Such a division between the suction noise device and the discharge noise device may prevent discharged refrigerant from unintentionally heating suctioned refrigerant, which may reduce suction loss. The formation of the suction and discharge noise devices using a plastic material may reduce fabricating costs, and the structures of the suction and discharge side noise spaces may be simplified and noise removal effects may be improved, reducing an overall size of the muffler and improving noise effects.