This paper presents a simple mathematical model of the turbidity current. The model consist of conservation equations for fluid mass and momentum and sediment volume. To describe the outline of the phenomena, we employed the boundary layer approximation and assumed the constant eddy diffusivity. The effect of the bottom shear and the resuspension of particles are neglected. In the numerical analysis, in addition to the finite difference method, the method of moment is also employed, which enables forward computation even in the case where the surface return flow is present. Flow velocity properties and sediment concentration distributions are given for various values of both dimensionless eddy diffusivity and the densimetric Froude number. Predicted velocity profile and sediment concentrations are compared with experimental data.