The conjugated straight-line internal gear pair, including a pinion with straight-line profile and an internal gear with profile conjugated to the pinion profile, is the key components to the conjugated straight-line internal gear pumps. Truninger [Truninger gear pump. Patent 3491698, USA, 1970] pointed that this kind of gear pairs leads to a very small trapped volume, which is 10 times smaller than that of the conventional involute internal gear pumps. Therefore, it can yield significant reduction in noise levels of the pumps. However, to the authors’ knowledge, there is no research on the design of these gear pairs until now. First, our study describes the straight-line profile of the pinion mathematically with definitions of some geometric parameters. Second, according to the theory of gearing, the mathematical models of the rack-cutter and the conjugated internal gear are derived. Then, the condition to avoid overcutting is obtained for the generation of the pinion by a rack-cutter. Finally, the condition to avoid interference in the internal gear pair is derived as a non-linear equation system and an algorithm is developed to find a numerical solution. Two examples are presented to demonstrate how to determine tooth numbers of the internal gears for avoiding interference. It is hoped that the study in this article should be helpful to the designers of the conjugated straight-line internal gear pairs. Moreover, it could provide a prepared knowledge for the researchers to investigate the performances of the fluid power gear machines, pumps, and motors, with the conjugated straight-line internal gear pumps.