Diffuse correlation spectroscopy (DCS) is a rapidly growing optical technology to noninvasively assess the tissue blood flow index. We develop a multichannel DCS topography system based on a multi-tau photon correlator, which comprises a long coherence length laser, a photomultiplier tube, and a photon correlator. The multi-tau photon correlator structure can obtain the intensity temporal correlation curve with high resolution and large dynamic range. Combining the imaging characteristics of the system, the constrained nonlinear optimization algorithm based on the analytical solution of the correlation diffusion equation is used as the model. The model is applied to match data between actual measurements and model predictions calculated by analytically solving the correlation diffusion equation in semi-infinite geometry. Finally, the dynamic phantom experiments demonstrate that the imaging system can distinguish different flow rates of liquid medium to reconstruct a two-dimensional image of flow rate distribution.