This study investigates infragravity motions on a two-dimensional fringing reef with a concave topography using a wave-resolving nonlinear Boussinesq wave model. The effect of bathymetric nonlinearity on spatial variations of infragravity waves is studied from shore-normal incident random waves. The model is first verified from cross-shore/alongshore significant wave height, wave setup and infragravity wave height measured in laboratory experiments. The modeled velocity is further examined to elucidate the infragravity-wave current field. Wavenumber-frequency velocity spectra show that cross-shore infragravity motions are controlled by the leaky waves, while alongshore infragravity motions exhibit edge waves characteristics. Additionally, high-mode edge waves prevail on the entire infragravity frequency band while low-mode edge waves are dominant at very low frequencies. Furthermore, the model results illustrate the spatial and temporal variability of wave-induced nearshore currents, alongshore and cross-shore flows accompanying with circulation cells and rip currents. The infragavity-wave current field is nearly identical to the mean current field and the circulations develop at the same spatial scale as the reef flat.