Abstract: Tuned mass damper (TMD) is a passive energy dissipation device widely used in structural vibration control, while its performance is sensitive to the uncertainty of system parameters. Robust optimal design enables reducing the sensitivity of the system response to uncertain parameters by minimizing the mean value and fluctuation of the system response simultaneously. A robust optimal design method is developed for TMD based on the intrusive polynomial chaos expansion (PCE) method. The uncertainty of system parameters is considered by orthogonal polynomials. The intrusive PCE method is exploited to analyze the statistical moments of the system response and establish the analytical expressions between the mean value and standard deviation of the structural response and the TMD parameters. Minimizing the maximum of the mean value and standard deviation of the structural response in the load frequency band is adopted as the optimization objective to determine the robust optimal parameters of TMD through a suitable optimization algorithm. To verify the effectiveness of the proposed method, a footbridge is taken as a numerical example to estimate the performance of TMD on pedestrian-induced vibration with consideration of uncertain modal parameters. The result shows that the developed method is extremely computationally efficient, and TMD designed by this method presents great control efficiency and robustness.