A fluid pump or air compressor with a wave transmission function is used for being connected with a prime motor so as to pump gas or liquid. The fluid pump or air compressor is characterized in that the fluid pump or air compressor comprises a shell unit, four fluctuation plate units and a center cam unit; the shell unit comprises a cuboid-shaped shell, load bearing and supporting columns and four runners arranged on the four side walls of the shell in parallel; the four fluctuation plate units are used for acting on gas or liquid entering the corresponding runners and arranged in the four runners correspondingly; each fluctuation plate unit comprises a plurality of fluctuation plates and a plurality of connection rods of the equal length, and the connection rods of each fluctuation plates are movably connected correspondingly; the center cam unit is arranged in the shell and comprise a center shaft and a plurality of quadrangular cam mechanisms; and the prime motor is connected with the center shaft and drives the center shaft and the multiple quadrangular cam mechanisms penetrating through the center shaft to rotate, the rotation movement of the quadrangular cams and a driven piece is converted to vertical movement of the connection rods which are of the same length and are connected with the driven piece, and the vertical movement of the connection rods of the same length drives the fluctuation movement of the fluctuation plate units so that gas or liquid can be compressed. The fluid pump or air compressor with the wave transmission function is simple in structure and long in service life, and meanwhile the operation process is stable.