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When the sediment and the dissolved matter laden in the river meet a clear water in reservoirs, the turbid water will plunge and spread into the clear water, forming the turbidity current and influencing the water quality and the life of the reservoir. Due to the unsteady nature of the flood, the turbidity current is unsteady. In the present study, we use the MIKE 3 computational fluid dynamics code to simulate continuous and discontinuous turbidity currents on a flat slope. With the model used by us, the turbulence is divided into two parts: the horizontal turbulence and the vertical turbulence, which are separately modeled by the Smagorinsky model and our model to capture the anisotropic turbulence. In this model, the sediment settling and deposition are considered. The simulation results concing the flume water surface level, the front velocity and sediment concentration profiles are found consistent with the experimental data, particularly, for the sediment concentration profiles with an absolute mean error of 0.026 kg/m3 and the root mean square error of 0.046 kg/m3. This finding suggests that this model can be used to well predict the turbidity current on the flat slope.