A numerical model that predicts the stratigraphy of a prograding Gilbert delta is presented. Such a Gilbert delta is formed when a river is flowing into a deep basin and the sediment transported by the river downstream avalanches downa steep slope.These deltas are characterized by thin and relatively low-slope topsets, steep foresets (the prograding slip faces), and thin, fine-grained bottomsets. Bedforms such as dunes, bars and Gilbert deltas prograde through avalanching of sediment down the slip face, in which a vertical sorting pattern develops, with the coarser sediment preferentially deposited at lower elevations. We describe the stratigraphy formed by such a prograding delta in case of a variable base level by coupling the Hirano active layer model for the topset to a lee face-sorting model for the foreset. Numerical simulations are performed at laboratory scale. Base level varies as a cosine function with constant amplitude and variable frequency, so representing cycles of base level. The main result is that low-frequency oscillations of base level are recorded in the stratigraphy of a Gilbert delta, which offers possibilities for future interpretations of base level variations from measured stratigraphy.