A novel cosine gear drive is presented in this paper. The pinion of the drive utilizes a cosine curve as the tooth profile. It takes the zero line of the cosine curve as the pitch circle, a period of the curve as a tooth space, and the amplitude of the curve as the tooth addendum. The generation principle of the cosine gear is described. The mathematical models, including the equation of the cosine tooth profile, the equation of the conjugate tooth profile and the equation of the line of action, are established based on the meshing theory. An example drive in solid model is presented and its computerized simulation is carried out. A few characteristics, such as the contact and bending stresses, the sliding coefficient and the contact ratio, of this new drive are analyzed. A comparison study of these characteristics with the involute gear drive was also carried out in this work. The results confirm that the cosine gear drive has lower sliding coefficients and the contact and bending stresses of the cosine gear are reduced in comparison with the involute gear.