Herein, we studied the mode characteristics of a few-mode fiber with an elliptical-core. We investigated the general expression of the Kerr nonlinear coupled-mode equations for the few-mode fiber and discussed the design process of an optical fiber parametric amplifier in detail. The dependence of the optical field mode distribution on core ellipticity was simulated using the COMSOL software, following which the phase mismatch factor in four-wave mixing and the corresponding mode field overlapping integral (or nonlinear coefficient) were calculated. In addition, we studied the degenerate four-wave mixing process of three mode groups in the elliptical-core few-mode fiber with a step refractive index distribution. The results show that when the LP21a-mode pump power is 0.5 W, the maximum gain of 20.15 dB can be obtained and the elliptical-core tolerance size is 0.6 μm in the gain deterioration range of 2 dB.