In this study, the seismic behavior of a laboratory steel structure with a moderate mass eccentricity, under simultaneous translational and rotational earthquake components is investigated using nonlinear incremental time history analysis. Seven three-component accelerograms recorded in type C soil were employed, and their rotational components were generated using wave propagation theory and elasticity relations via MATLAB. A 5-story steel frame, with and without mass eccentricity, was modeled in ANSYS, and both models were analyzed under three-component and six-component excitations. According to the analysis results, it is observed that not considering the independent rotational components of ground motion in the dynamic analysis of a structure with mass eccentricity cannot accurately estimate the effects of the interaction of translational and rotational responses. So that in most cases, the response of structures with and without mass eccentricity under six-component excitation was on average about 40 percent greater than the results obtained from dynamic analyses under three-component excitation. In addition, in all analyses, the departure from the center of mass has a significant impact on all structural responses and the probability of its failure. More specifically, such impact is about 45 to 55 percent on all structural responses and the probability of its failure.