This work presents a novel sequential sampling approach to the multi‐objective reliability‐based design optimization of moment‐resisting steel frames subjected to earthquake excitation. The optimization problem is formulated with two objective functions, namely, the total mass and the energy dissipated by beam members of the frame, and subject to uncorrelated probabilistic constraints on dynamic responses under the effects of correlated random parameters of floor masses, external loads, and material properties. The dynamic responses for a small number of designs are found by nonlinear response history analysis and further approximated by Gaussian process (GP) models to mitigate the computational burden during the optimization process. Approximate solutions sorted among existing candidate solutions are updated after each optimization iteration using discrete random local and global searches. The GP models are also refined after each optimization iteration by specifying new sampling points that lie on the Pareto front of a bi‐objective deterministic maximization problem formulated for the improvement in the current approximate solutions and the feasibility of the new sampling points. As demonstrated in a test problem, the new sampling points tend to distribute in the neighborhood of the exact solutions, thereby underpinning a quick termination as well as the robustness of the proposed method. Optimization results from the test problem and a design example show that good approximate solutions are always obtained as the solution quality converges.