Piezoelectric acoustic devices that are integrated with semiconductors can leverage the acoustoelectric effect, allowing functionalities such as gain and isolation to be achieved in the acoustic domain. This could lead to performance improvements and miniaturization of radio-frequency electronic systems. However, acoustoelectric amplifiers that offer a large acoustic gain with low power consumption and noise figure at microwave frequencies in continuous operation have not yet been developed. Here we report non-reciprocal acoustoelectric amplifiers that are based on a three-layer heterostructure consisting of an indium gallium arsenide (In0.53Ga0.47As) semiconducting film, a lithium niobate (LiNbO3) piezoelectric film, and a silicon substrate. The heterostructure can continuously generate 28.0 dB of acoustic gain (4.0 dB net radio-frequency gain) for 1 GHz phonons with an acoustic noise figure of 2.8 dB, while dissipating 40.5 mW of d.c. power. We also create a device with an acoustic gain of 37.0 dB (11.3 dB net gain) at 1 GHz with 19.6 mW of d.c. power dissipation and a non-reciprocal transmission of over 55 dB.