This paper presents an experimental study on scour at complex bridge piers exposed to combined waves and current. Regular waves were produced with various strength and superimposed on co-directional current with constant velocity. The key parameters tested and discussed include Keulegan-Carpenter (KC) number, relative current strength U-cw, pile-cap elevation, and pier skewness. The scour hole patterns and scour mechanism were found to depend on the flow type combination, and, compared with steady current, the superposition of waves may restrain the development of scour hole due to migrating bed-forms. Three types of scour temporal evolution (i.e. ascend-descend, asymptotic, and transferred type) were identified, and the scouring processes (structure exposure, cyclic sediment motion, etc) at the scour initiation and development stages were also discussed. The dimensional time scale decreased for higher bed mobility with a power functional relationship, while the non-dimensional time scale peaked when the maximum near-bed velocity components contributed by current and waves are similar. The dependence of the equilibrium scour depths, both original and normalized, on the tested parameters was also analysed. It was found that the normalized scour depth at complex piers increases with greater KC and U-cw and tends to be much larger than that for single piers. The increase of bed mobility did not lead to scour peaks at the clear-water threshold as what is usually observed for current-only scour. The influence of pile-cap elevation on the equilibrium scour depth was found to be much weaker than that under steady current. Furthermore, new scour prediction method is proposed to incorporate extra terms taking the influence of pile-cap elevation and pier skewness into account. The prediction accuracy is improved significantly. Finally, more suggestions regarding design considerations are also given.