Electronics cooling is a critical issue affecting technological development. Parallel micro-channel heat sink (PMCHS) is widely applied for electronics cooling. However, the existing optimization methods are incapable to perform efficient design of three-dimensional liquid-cooled PMCHSs, impeding the thermal management of high power and volume-shrinking electronics. In this study, a flow resistance network (FRN) model is developed for structural optimization of three-dimensional liquid-cooled PMCHSs. Based on the uniform flow rate distribution, the FRN model is used to determine the optimized parallel channel widths and the optimized inlet deflector shape of the PMCHS. With the optimized parallel channel widths, the maximum temperature (Tmax) of the PMCHS is decreased by 4.0 K and the temperature standard deviation (σT) is decreased by 20%. With the optimized inlet deflector shape, Tmax and σT are reduced by 4.8 K and 14% respectively. The optimization method based on the developed FRN model for structural design of PMCHSs avoids multiple iterations of system parameters in existing optimization methods, showing its potential in high efficient thermal management of electronics.