The characteristics of time-dependent Brillouin-enhanced four-wave mixing (BEFWM) interaction were investigated. The temporal and spatial profiles of four optical waves and an acoustic wave in the BEFWM interaction of polarization-decoupled, anti-Stokes type were calculated using a relatively simple simulation method. In the simulation with step-function optical waves, two distinctive interaction regimes were observed: steady-state regime and reconversion regime which are distinguished by their characteristic temporal behaviors. The simulation with pump waves similar to the BEFWM experiment of polarization-decoupled, anti-Stokes scattering type showed that the temporal shape of the output signal well matched with the observed result.