Optoacoustic (OA) imaging is an emerging technology that combines the high optical contrast of tissues with the high spatial resolution of ultrasound. Taking full advantage of OA imaging requires a better understanding of OA wave propagation in light-absorbing media. Current simulation methods are mainly based on simplified conditions such as thermal confinement, negligible viscosity, and homogeneous acoustic properties throughout the image object. In this study a new numerical approach is proposed based on a finite-difference time-domain (FDTD) method to solve the general OA equations, comprising the continuity, Navier-Stokes, and heat-conduction equations. The FDTD code was validated using a benchmark problem that has an approximate analytical solution. OA experiments were also conducted and data were in good agreement with those predicted by the FDTD method. Characteristics of simulated OA waveforms and OA images were discussed. The simulator was also employed to study wavefront distortion in OA breast imaging.