A rock slope, known as the Checkerboard Creek slope located in British Columbia, Canada, is moving under the effect of seasonal temperature changes. Freezing and thawing processes are causing the rock to move at rate of 13 mm/year. A 60 m deep weathered zone has been identified along the slope. This paper uses a discrete element numerical modeling approach to investigate the Checkerboard Creek slope, which is moving toward the reservoir, and to propose a support system to stabilize the slope. The numerical simulation conducted in this study shows that the failure is situated near the slope's toe where a road-cut has been made. To stabilize the rock slope, a support system comprising of cables and a shotcrete layer was proposed and installed numerically along the steepest portion of the weathered rock area. Comparison studies showed that the proposed support system could successfully stabilize the moving rock slope at a reduced tensile strength value. By using this support system, the risk of rock slope failure will be reduced to an acceptable limit through increasing the Factor of Safety of the slope to 1.15. Installing a support system for this problematic slope is highly recommended.