In order to establish the design method of a noncircular face gear (NFG) with intersecting axes, the meshing theory of this gear is investigated based on the principle of space gear meshing. A generalized approach for designing closed pitch curve of the NFG with intersecting axes is proposed based on Fourier series. The mathematical model of the NFG generated by a shaper cutter is established. The fundamental design parameters of the gears are defined, with the principle for determining their values discussed. The results of simulation and experiment verify the feasibility of the novel transmission mechanism and the correctness of the mathematical model of NFG with intersecting axes.