As the development of gear pump with high pressure, large flow and low noise, a high-order elliptic gear pump with low trapped oil and less pulsating is proposed in this paper. The corresponding section curve model was established. By comparing 3-3 combination with 3-3-3 combination in terms of rate of flow and flow pulsation, the 3-3-3 combination was used as the main structure of high-order elliptic gear pump. The elliptical gear ratio has a certain change rule. Each tooth has a specific meshing position. Coordinate transformation method has been used to analyze the high-order elliptic gear tooth profile equation, which provides a theoretical basis to establish CAD modeling and simulation analysis.