In order to control the linear polarization (LP) mode in few-mode erbium-doped fiber amplifiers (FM-EDFAs), the dependence of mode field distribution and effective refractive index in optical fibers with elliptical cores on the elliptical parameter (the ratio of the major to minor axis length of the elliptical core) is investigated by multi-physics field simulation software. When the elliptical parameter is more than 1.050, TM₀₁ and HE_21o, as well as TE₀₁ and HE_21e can be expressed by LP₁₁ odd and even modes which have an effective refractive index difference of larger than 10^-4, with negligible mode crosstalk. This paper approximately constructs the mode field in an optical fiber with an elliptical core through the superposition of the LP modes, and compares the gain errors calculated by the approximate LP mode field and the precise mode field in the active fiber with an elliptical core. When the elliptical parameter is less than 1.250, the three-mode gain error calculated by the approximate LP mode field is smaller than 0.5 dB. The results show that the approximate LP mode field can greatly reduce the design complexity of FM-EDFAs with elliptical cores during analysis.