The rotary compressor is widely used in the air conditioner because it is efficient and compact. Recently, the need for silent and efficient compressors is much stronger than the past. The new type muffler was invented to reduce the noise level and to improve the efficiency. The new type muffler that has two side discharge holes and dome shape resulted in much lower overall noise level, especially noise levels around 1kHz than the old type one of one center discharge hole in the acoustic spectra. Also it showed a higher efficiency of air conditioner by lowering oil discharging amount of a compressor than old type one of a rectangular shape and two side discharge holes. The noise reduction and efficiency improvement by the new type muffler were verified by tests for votary compressors and air conditioners.