The motion of 2D gravity currents on a horizontal bed is simulated by a Large Eddy Simulation (LES) model. The gravity currents consist of either a mixture of nearly uniform sized particles or saline water.The numerical model uses cubic spline method for space derivatives and Crank-Nicolson scheme with fractional step for marching in time. The eddy viscosity is computed by Smagorinsky method modified to include effects of buoyancy. The simulated results are compared with experimental data for front height, front propagation speed and front buoyancy. The computed densimetric Froude number at the front is compared with experimental value as well as that available from existing empirical and experimental studies. The numerical model shows promising results for simulation of gravity currents and understanding front characteristics.