The disc filter with discrete flow channels is a novel device that produces a relatively small water head loss. The regular distribution of the convex structures on the disc surface is one of the main factors affecting head loss of the disc filter. In order to find out the influence of different types of the convex structure on the internal flow field and further reduce the head loss of the disc filter, a physical experiment and numerical simulation were conducted to analyze the head loss and flow field distribution characteristics of five different convex structures, including the original right triangle, rhombus, oval, upper triangle and lower triangle. The results show that the lower triangle is conducive to reducing the contact length between the convex structure and the main flow zone and the turbulence kinetic energy intensity, as well as the head loss of the disc filter with discreet flow channels. Compared with the original right triangle, the contact length and maximum turbulence kinetic energy of the four optimized convex structures decreased by 9.61%-36.73% and 25.87%-49.96%, respectively, among which, those of the lower triangle decreased by 29.99% and 49.96%. According to the simulation, the head loss coefficient of the right triangle was the largest, and that of the lower triangle was the smallest, which also had the highest energy conversion efficiency. Under clear water condition, the head loss of the disc filter with lower triangle structure decreased by 14.89%-21.93% compared with the original structure. The research findings can provide some reference for the structural optimization of disc filters with discrete flow channels.