A silencing device and a compressor having the silencing device are disclosed. The silencing device has a housing. An air inlet and an air outlet are provided to the housing. An air flow channel is provided in the housing for allowing air communication between the air inlet and the air outlet. An oil hole is provided in the housing for discharging oil from the housing. An oil guide part is arranged on the outside of the housing and at a position downstream of the oil hole in the moving direction of the oil, such that the oil drips from the housing after flowing from the oil hole to the oil guide part.