A horizontal two-dimensional finite element model is developed in order to estimate the process of scour around a large-scale cylinder due to waves. The present model differs from previous models in the sense that the wave model is based on an elliptic mild slope equation and the sediment transport induced by the steady streaming is considered. The current induced by the gradient of radiation stress is considered and calculated using a depth integrated shallow water equation. The contributions of the Lagrangian drift velocity to the scour is also considered in this model. The model is validated against a few cases where experimental data are available. The comparison of the calculation results with the experimental data indicates that the present numerical model predicts the scour around a large cylinder reasonably well. The effects of Keulegan-Capenter (KC) number, the grain size of sediments and the model scale on scour around a large cylinder are also investigated.