The invention relates to an encapsulated electrically driven compressor for a motor vehicle and has an object to prevent electrical parts for connecting an electric motor housed in a hermetically sealed housing to an outside electric control circuit from being easily contacted with liquid-phase refrigerant, which has a higher electrical conductive property than gas-phase refrigerant. According to one of features of the present invention, an encapsulated electrically driven compressor comprises a hermetically sealed housing, a compressor device for compressing refrigerant of a refrigerating cycle, an electric motor for driving the compressor device, and a connecting device having a terminal casing for covering electrical conductive terminal portions which connect the electric motor with an outside electric control circuit, wherein the compressor device, the electric motor and the connecting device are encapsulated in the hermetically sealed housing. The terminal casing is air-tightly fixed to a side wall of the housing and a small opening is formed in the terminal casing at a position which is lower than a position of the electrical conductive terminal portions by a predetermined distance (in a downward direction towards an inside space of the hermetically sealed housing).