In this study, we investigated the local scour around a large pile, termed the umbrella suction anchor foundation (USAF), under nonlinear waves and current. We developed a wave-foundation-seabed coupled model and analyzed the characteristics of the flow field, turbulence characteristics, and scour depth evolution, and the influence of wave height and anchor branches on local scour. The results indicate that the horseshoe vortex increases turbulence intensity around the offshore edge of USAF, amplifying the shear stress on the seabed, which causes local scour around the USAF upstream. The anchor branches protected the soil from scouring to some extent. The scour and accretion depths increased rapidly at the initial stage, and then, the scour rate decreased. After approximately 300 wave cycles, the scour and accretion depths gradually stabilized. The changing trend of the scour evolution with wave height converged, but higher wave heights resulted in larger scour and accretion depths simultaneously.