Focusing light though scattering media beyond the ballistic regime is a challenging task in biomedical optical imaging. This challenge can be overcome by wavefront shaping technique, in which a time-reversed (TR) wavefront of scattered light is generated to suppress the scattering. In previous TR optical focusing experiments, a phase-only spatial light modulator (SLM) has been typically used to control the wavefront of incident light. Unfortunately, although the phase information is reconstructed by the phase-only SLM, the amplitude information is lost, resulting in decreased peak-to-background ratio (PBR) of optical focusing in the TR wavefront reconstruction. A new method of TR optical focusing through scattering media is proposed here, which numerically reconstructs the full phase and amplitude of a simulated scattered light field by using a single phase-only SLM. Simulation results and the proposed optical setup show that the timereversal of a fully developed speckle field can be digitally implemented with both phase and amplitude recovery, affording a way to improve the performance of light focusing through scattering media.