Sliding on gear teeth working surfaces has negative effects on the performances of gears, such as tooth surface wear, pitting, etc. In order to reduce the gear sliding during high speed and heavy load, a new type of pure rolling gear, named as an asymmetric logarithmic spiral gear, is designed referring to the characteristics of the Issus planthopper gear. To explore the meshing principle of this kind of gear, the equations of the teeth surfaces, their working lines, and contact lines are all derived. Then, the tooth profile parameters and slip rate are calculated. To ensure accurate gear engagement, the gear interferences are analyzed to build the gear models. Subsequently, the gear is performed to simulate its working condition by the finite element method. Furthermore, the results are compared with that of the pure rolling single arc gear. As a result, the asymmetric logarithmic spiral gear behaviors less contact and bending stresses than the pure rolling single arc gear under the same work condition.