The velocity field of the flow over a curvilinear broad-crested weir is measured using a one-dimensional laser Doppler anemometry (LDA) for two different flow conditions. Using standard k-epsilon, realisable k-epsilon, renormalisation-group k-epsilon, shear stress transport k-omega and Reynolds stress model, the basic equations are solved by ANSYS-Fluent package program based on finite volume method for the same experimental conditions. The volume of fluid (VOF) method is used to compute the free surface of the flow. Grid convergence index (GCI) is performed to examine the effect of the selected grid structure on the numerical results. Experimental results of the velocity field and flow profiles are compared with the numerical results for validation purposes. The comparisons of the numerical and experimental results show that the renormalisation-group k-epsilon turbulence closure model predicts the velocity field and flow profiles more accurately compared to those of the other models used in the present study.