In nature, such as sunflowers, nautilus shells, tornadoes, and star trajectories appear as logarithmic spiral shape structures, which are closely related to the properties of logarithmic spirals such as fixed angle, curvature gradient increasing, and self-similarity. Inspired by the phenomenon of logarithmic spiral in nature, a novel gear transmission with logarithmic spiral as tooth profile is proposed herein. Based on the characteristics analysis of the logarithmic spiral, the mathematical model of the logarithmic spiral conjugate tooth profile is derived, and then the meshing process of logarithmic spiral gear pair is numerically simulated. Finally, in order to assess the contact and mechanical properties of the new gears, the test samples of gear pairs are fabricated, and contact patterns and bending fatigue strength tests of the new gear pairs are also carried out. The results indicated that the logarithmic spiral gear has the characteristics of constant pressure angle transmission, and its meshing process is continuous and without meshing interference. The contact condition of the tooth surface is good, and the contact form is line contact. Compared with the involute gears, the logarithmic spiral gears have a long life and high bending fatigue strength of the tooth roots, which demonstrates the feasibility of the proposed gear drive. The research can provide certain theoretical support for the high-performance gear transmission system design.