This study proposes an adjustment to the design of spillway control section of a water supply dam project in Kenya which is constrained by flood discharge requirements, geological conditions, land use scale, power supply capacity, and dam operation and control. The proposed design scheme changes from a gated wide-crested weir to a labyrinth weir to ensure the flood discharge capacity meets the original design requirements and reduce project costs while minimizing impacts on the dam works. Design parameters such as the height, width, and extended length of labyrinth weir are preliminarily proposed based on engineering experience. Flow-3D software is used to simulate and analyze the spillway discharge conditions, and physical model tests are conducted to verify the design parameters determined from the numerical simulation results. The numerical simulation and physical model test demonstrate that when the water head above the weir is less than the weir height, the comprehensive flow coefficient of the labyrinth weir initially increases and then decreases with increasing water head above the weir. Moreover, no distinct unfavorable flow regime was observed during labyrinth weir discharge, reflecting sound discharge capacity that meets the special requirements of the engineering application.