Traditional pumps cannot have both high pressure and high flow performance at the same time. In order to solve this problem, a rotary eccentric extrusive pump was designed which has the characteristics of high flow rate of the centrifugal pump and high pressure of the reciprocating pump. In this study, the principle and design method of the rotary eccentric extrusive pump were put forward. The expressions of the inner envelope line of the cylinder and rotor profile were deduced. The size and position of the inlet and outlet, the material and force of the crankshaft, and the sealing system of the rotor underwent rationality analysis. A test of the rotary eccentric extrusive pump was carried out, and the curve of flow-time and pressure-time, the variation of volumetric efficiency, mechanical efficiency, hydraulic efficiency, and total efficiency with the change of outlet diameters and motor rate were analyzed. The results show that when the input power was 17.6 kW and the motor RPM（Revolutions Per Minute）was 800 r/min, the flow of the test pump reached 32.17 m³/h and the pressure reached 1.7 MPa. The hydraulic efficiency increased with the increase of RPM and reached a inflection point when the RPM reached 800 r/min. When the RPM was within 800 r/min, the non-uniform coefficient of flow was less than 2.4%, the volume efficiency was above 85%, the maximum of mechanical efficiency was 90.23%, and the overall efficiency reached a maximum of 60.75%. The rotary eccentric extrusive pump is characterized by high pressure and high flow performance at the same time, and is worthy of promotion and application.