Focusing on solving the structural problems of trapped-oil phenomenon and large flow ripple in external gear pump, based on transmission advantage of involute gear and its forming principle, the contact ratio of 1 and root point of tooth profile located on base circle were used as the limiting conditions, and tooth number was the only design construction parameter, a reverse construction method of involute tooth profile without trapped-oil and undercut was proposed. A new axial double gear pair structure was designed to solve the structural problem of large flow pulsation of the original single gear pairs. The results show that the reverse design method is simple and accurate; when the contact ratio of single gear pair is 1, no trapped oil phenomenon can be ensured; when the root point of the tooth is located on the base circle and the modification hobbing is adopted, no root cutting phenomenon can be ensured; the constant flow ripple coefficients of single gear pair 0.375 and double gear pair 0.094 are independent of the teeth number, which is beneficial to adopt the high volume utilization coefficient 0.35 of six-tooth number gear, and the pump has better lightweight effect; double gear pairs assembled by axial dislocation and interval with 180° divided by tooth number is easy to achieve, and when the following axis comprehensive contact ratio equales to 2, the transmission stability can be ensured.