The solitary evolution and deflection of matching Gauss beam have been investigated in biased dissipative photovoltaic-photorefractive crystals. For a given dissipative system that supports a determinate dissipative screening-photovoltaic soliton (DHSP), one call find a corresponding Gauss beam which matches with the system parameters, which will evolve into a steady-state spatial soliton and propagate steadily in the given dissipative crystal. At the same time, we have investigated the impact of diffusion on the propagation (or solitary evolution) of the matching Gauss beam in the dissipative system. It is indicated that the diffusion effect can cause deflection of the matching Gauss beam during the transmission, and the deflection process is extremely similar to that of the corresponding DHSP soiliton. By comparing the two deflection results, we found that for the matching Gauss beam, the numerical result of deflection is close to the analytical result of the bright DHSP soliton. In a word, the solitary evolution and propagation (including the deflection) of the matching Gauss beam is quite close to those of the DHSP in the dissipative system.So the matching Gauss beam can be used as the incident beam to replace the bright DHSP beam, which is more convenient in theory and experiment.