In the design of a steel moment resisting frame, uncertainties may arise from a variety of sources, such as ground motion, mass, and damping ratio, etc., that may cause variation in seismic demand and capacity. These uncertainties need to be taken into account to ensure the desired margin of safety for required performance objectives. FEMA 350, a reliability based design guideline, can be employed to mitigate safety concerns by satisfying minimum confidence level requirements for performance objectives. However, in these existing design codes, variation in seismic demand is not explicitly considered in the design process. According to the FEMA 350 procedure, seismic demand is calculated with a suite of seismic records, considering ground motion variability, while only median demand is used in the subsequent calculation of demand to the capacity ratio and confidence level. In this paper, variation of seismic demand due to ground motion variability is considered explicitly as a robustness measure, and the mean value of seismic demand is treated as a safety measure. A Robust Design Optimization of steel moment resisting frame methodology is proposed, which is featured as a multi-objective optimization problem with the variation of seismic demand, mean value of seismic demand and cost as three objectives. In the optimization problem, optimal steel section sizes are sought to minimize these three conflicting objectives. The proposed methodology is then demonstrated through a multi-story multi-bay steel moment resisting frame design and solved with a Non-dominated Sorting Genetic Algorithm-II. With three competing objectives, the proposed methodology provides a set of designs in the form of a Pareto Front, which is robust, safe and economical. Furthermore a uniformity drift ratio requirement is proposed to ensure efficient designs.