<p>The quantification of uncertainties in various forms must be considered for the safe operation of offshore floating structures because the surrounding environment is inherently stochastic and ever-changing. Uncertainties in loads applied on structures can arise from two main sources: long-term and short-term uncertainties. Long-term uncertainty results from the changing sea states (conditions that change several times each day), while short-term uncertainty results from irregular wave characteristics that prevail during any of these sea states that might last from, say, 1 to 6&#xa0;h. To address these uncertainties in an efficient manner, this study proposes a surrogate modeling method combined with a dimension-reduction approach to predict the long-term extreme response of an offshore floating structure. A subject of particular interest is one of accurate prediction of response levels associated with a low occurrence probability. The proposed method consists of two steps: (1) model order reduction in the frequency domain for the short-term response analysis and (2) gradient-based stochastic dimension reduction for the long-term dynamic response analysis. For efficiency, polynomial chaos expansion is used to construct surrogate models based on the reduced-dimension representation. Surrogate model-based extreme response predictions are compared with full-blown and costly Monte Carlo simulation results obtained using the original (truth) model. Accuracy and efficiency are demonstrated through numerical examples.</p>