The invention discloses a displacement pump and a conveying method thereof. The displacement pump comprises a rotor, a shell, a transmission shaft, first check valves, second check valves and a transmission connection part. The cross section of the radial outer contour of the rotor is in the shape of a reuleaux triangle, and the rotor is provided with a groove containing the transmission shaft and the transmission connection part. The cross section of the radial inner contour of the shell is square, and the shell is provided with a support line with the width equal to the width of the reuleaux triangle rotor. The transmission shaft is provided with a sliding groove. The first check valves and the second check valves are arranged at the four corners of the shell correspondingly and are installed in pairs reversely. One end of the transmission connection part is located in the groove matched with the radial center of the rotor, and the other end of the transmission connection part is connected with the sliding groove of the transmission shaft. According to the displacement pump and the conveying method thereof, the number of wearing parts is small, the displacement pump has the advantage of stable flow, and a large selection range is provided. In addition, fluid from different sources can be conveyed accurately according to a certain proportion, and the requirements for the reliability, economy and flexibility of the pump in actual production can be met.