A central refractive index depressed few-mode erbium-doped fiber (FM-EDF) can change the number and cut-off order of transmission modes, and has an excellent performance in terms of mode field modulation and gain equalization. In this paper, the equivalent refractive index theory is employed to describe the cut-off characteristics of optical fiber modes, and the changes of modes during the transition from the traditional step-index fibers to ring-core fibers are studied. The results show that when the central depression is larger than 0.012, the optical fiber only supports LP_n1 mode transmission and makes the field energy of LP₀₁ mode shift away from the central areas. Additionally, when the optical fiber is used in signal amplification areas, and there is a corresponding linear relationship between the refractive index depression and the radius of the doped region, the differential modal gain can be kept below 2 dB. A homemade central depressed FM-EDF is used to test the gain characteristics of LP_n1 mode. The experimental results show that the gain of all signal modes is higher than 18 dB, and the differential modal gain is 1.3 dB.