In this paper, novel non-involute cylindrical gears are designed based on a curved path of contact. Firstly, a parabolic curve is predesigned as the contact path of novel gears. Then, the tooth profiles of the novel gears are calculated using differential geometry and spatial meshing theory. Secondly, the three-dimensional tooth models of the novel non-involute gears are established according to a machining simulation. Thirdly, a simulation model (including misalignment error and longitudinal modification) is established to analyze the performance of the novel non-involute gears. Finally, an example is given, and the results show that the presented novel non-involute gears have greater load-carrying capacity compared with the involute gears. Moreover, whether modified or not, with or without misalignment error, the stresses of the presented novel gears are lower than those of involute gears.