Acoustic and electrical characteristics of biological tissue are important factors in magnetoacoustic tomography with magnetic induction (MAT-MI). Acoustic inhomogeneity significantly affects the propagations of sound waves. Differences in sound speed lead to distortions of the sound sources in the reconstruction process. The objective of this study is to develop a novel algorithm to reconstruct the sound source distribution in an acoustically inhomogeneous medium. The proposed algorithm is developed on the basis of the finite-difference time-domain method and time-reversal acoustic theory; it combines the relationship among symmetrical transducers with the back-projection algorithm. An acoustically inhomogeneous model with different regions of variable sound speeds is established to validate the proposed algorithm. From the data collected by a rotated focused transducer, first, the sound speed distribution is reconstructed, and then, the sound sources of the model are reconstructed. The reconstructed sound sources are obviously distorted when the speed differences are not considered. In contrast, the proposed algorithm yields reconstructed sound sources that are consistent with the model in terms of shape and size. Thus, the proposed algorithm is capable of accurately reconstructing the acoustic sources distribution in an acoustically inhomogeneous medium. This method provides a solution reducing the influence of acoustic inhomogeneity in MAT-MI. The distributions of sound speed can be obtained during the process of reconstructing the sound source. Consequently, the imaging of the acoustic speed and the electrical conductivity of biological tissues can be implemented simultaneously in MAT-MI.