Sustainable multi-story building designs are gaining increasing attention in light of the green development of the building industry. Recently, many studies have been conducted to determine the optimized embodied energy considering size of structural members and materials strength using a single objective function. In this context, the current study adopted a multi-objective function based on cost and Embodied Energy (EE) for the sustainable design of the entire multi-story building. A BuildingEnergy computer program is used to assess the energy consumption performance of a multi-story reinforcement cement concrete building. Based on the proposed method, an analysis is carried out to compare the optimal solutions for multi-story building. Furthermore, a detailed parametric study was conducted to explore the main factors for energy-efficient column and beam design. The results revealed that with a comparison of the most “carbon-friendly” and “cost-friendly” solutions, an added cost of 6–7% can contribute up to a 13% emission reduction. The sectional dimensions, steel rebar, concrete strengths, cost ratio, building height, and eccentricity remarkably influence sustainable design, cost optimization, and minimum carbon emission. Overall, this study could help to define cost-effective and energy-efficient structural members. Eventually, the EE is confirmed to be a feasible parameter for designing more sustainable multi-story RCC buildings.