Motivated by the analysis of a two-way functional data, the Spanish mortality data, we propose a novel robust functional singular value decomposition method. The regularized method smoothes the estimated singular column and singular row. In addition, this smoothing technique downweights the outlying effects slightly. The incorporation of robust method further reduces the outlying effects. A GCV method is developed for the smoothing parameter selection. Simulations are conducted to illustrate the usefulness of this new method.