The microchannel heat sink is a commonly used structure in mechanical cooling systems for microelectronics. Based on bionics, a simplified heat sink with a spider-web design is proposed in this paper. Under the condition of bottom heat flux q = 100 W/cm2 and Reynolds number (Re) = 442-884, the influence of three parameters (main channel width, branch width and rib width) on the performance of a spider web microchannel heat sink (SW-MCHS) under different Re conditions was numerically analyzed by computational fluid dynamics. The results showed that the main channel had the greatest influence on the Nusselt number (Nu) and the Euler number (Eu); With the increase of main channel width, Nu increased by 46.97%, and Eu decreased by 31.74%. Rib width had the smallest influence on Nu and Eu; AWith the increase of rib width, Nu decreased by 7.18%, and Eu decreased by 12.00%. Based on the research results, the correlations for predicting Nu and Eu of the SW-MCHS were fitted; the Radj2 values for the two correlations were 0.9523 and 0.9246, respectively. These fitting correlations could be used to predict Nu and Eu for the SW-MCHS. The present study has contributed to advancing the applications of microchannel heat sinks and enhancing the cooling efficiency of mechanical microelectronics cooling systems.