A vaneless contra-rotating compressor with multiple contra-rotating interfaces and application of the vaneless contra-rotating compressor is provided, which includes at least two vaneless contra-rotating interfaces. For each of the at least two contra-rotating interfaces, the contra-rotating interface corresponds to two of vaneless contra-rotating rotors. A rotating direction of an upstream rotor of the two vaneless contra-rotating rotors and a rotating direction of a downstream rotor of the two vaneless contra-rotating rotors are opposite. Rectifier stator vanes are not provided among all the rotors to supply sufficient inlet negative pre-swirl for the downstream rotors through the upstream rotors. Only the outlet guide vanes of the last stage, of the vaneless contra-rotating rotors are provided. The number of stages and the number of vaneless contra-rotating interfaces may be set flexibly according to the actual pressurization requirements.