In the field of free-space optical communication (FSOC), the sensitivity of the receiver can be affected by atmospheric turbulence, leading to light-intensity scintillation or beam drift. This paper offers a solution to this challenge by proposing a few-mode heterodyne receiver with a few-mode optical fiber amplifier (FM-OFA). The FM-OFA is used in the few-mode heterodyne receiver to enhance the output power of different modes of signal light, and the amplified signal light is detected by the few-mode heterodyne detection based on Kramers–Kronig (KK) relations, which effectively suppresses the atmospheric turbulence effect and improves the sensitivity of the receiver. In addition, we build an FSOC system and verify the sensitivity performance of this receiver under different turbulence conditions. The experimental results show that the sensitivities of the few-mode heterodyne receiver with an FM-OFA are −42.6dBm, −41.3dBm, and −40.7dBm, respectively, which are 8.8 dB, 8.5 dB, and 9.3 dB higher than those of the few-mode heterodyne receiver without an FM-OFA at average BER = 10−3 under low, moderate, and high turbulence intensities.