We simulated an improvement in fiber characteristics, specifically the differential modal gain (DMG) and the LP11 mode wavelength dependent gain (WDG) characteristics. We defined the DMG as the gain difference between the C-band wavelength-division multiplexing signal channels of the LP01 and LP11 modes at the shortest wavelength, and WDG was the gain difference between the signal gain of the LP11 mode at the shortest and longest wavelengths, when the DMG of the LP01 mode was zero. We achieved this improvement by changing the erbium doping distribution in ring-core erbium-doped fiber (RC-EDF), which has been attracting attention as an amplification medium for a 2-mode (LP01 and LP11 modes) erbium-doped fiber amplifier for mode-division multiplexed transmission. We applied an α-th power profile, trapezoid profile, and right and left triangular profiles to the RC-EDF. We found that the DMG value changed from negative to positive despite the value of the LP11 mode WDG being positive, and confirmed that the DMG could be adjusted by changing the distribution. We show level curve maps of the DMG, LP11 mode WDG, pump power, and EDF length on the allowable 2-signal-mode area map for inner and outer radius combinations of the RC-EDF, and clarify that it is possible to realize a region that provides high-efficiency amplification with a low DMG of <|0.1|  dB and a low WDG of <0.1  dB. Furthermore, we show that by varying the distribution of the erbium doping concentration, we can greatly change the position of the region on the map of the allowable 2-signal-mode area.