Gears are common and important components of many types of propulsion systems applied in mechanical engineering. The aim of this paper is to present the mechanical design and performance analysis of a novel two-stage magnetic precession gear (MPG). The main advantage of the proposed design is the ability to obtain higher transmission ratios than other currently known magnetic gear types. A detailed analysis of the performance of the MPG was carried out employing a developed numerical model of the magnetic field in the proposed gear. The MPG model is based on the finite element method (FEM) and allows determining the relations between the torque acting on the main components of the gear, load angles, and air-gap lengths. To validate the developed FEM model, the prototype of an MPG with a 1/144 gear ratio was built and tested. The experiments were also focused on determining the mechanical efficiency as well as the influence of rotational speed and lengths of air gaps on the maximum load torque. The tests indicated that the maximum efficiency of the studied MPG is about 30%, which is comparable to the efficiency of mechanical two-stage precession gears with face meshing.