Two-stage regeneration recycling water networks can effectively reduce regeneration cost without increasing freshwater consumption. The graphical approach can intuitively show the relationship between system parameters. However, existing researches only focus on the two-stage regeneration water network with series structure. In this paper, the two-stage regeneration recycling water network with parallel structure has been studied, and the graphical approach has been established to determine the targets, including the optimal flowrates and the optimal regeneration concentrations. The optimal flowrates containing freshwater and regenerated water of all stages, determined in order from good to bad according to water quality. A case study shows that regardless of the relative level of the regeneration concentrations in the first and second stages, the optimal flowrate targets are the same, but the optimal regeneration concentrations are different. Water networks with higher second stage regeneration concentration have lower regeneration cost.