Abstract: A finite-difference time-domain (FDTD) method is proposed to exactly calculate the sound field of the thermoacoustic tomography (TAT) with the inhomogeneous acoustic speed. Firstly, the basic equations of the TAT are discretized to differential equations by the FDTD. Then the electromagnetic pulse is modified twice in the simulation process in order to eliminate the error introduced by high frequency electromagnetic waves. It is shown by computer simulation results that the FDTD method has better accuracy than the time-of-flight method, which is in the common use, in the TAT with the inhomogeneous acoustic speed. When the acoustic speed difference is larger than 50%, the error of the FDTD method is ten times smaller than that of the time-of-flight method under the simulation condition. Therefore, this FDTD method is an efficient one for the sound field simulation of the TAT and can provide the theoretical basis for reconstruction algorithms of the TAT with the acoustic speed heterogeneity.