Turbidity current over a Gaussian-bump is investigated numerically using the upwinding combined compact difference (UCCD) scheme and the immersed boundary (IB) method in Cartesian grids. In the prediction of lock-exchange gravity-driven flow motion, the initial discontinuous concentration field is smoothed to avoid numerical oscillation by solving the Hamilton-Jacobi equation. The UCCD spatial scheme with sixth-order accuracy which introduces less dispersion errors is then used to discretize advection and diffusion terms in the calculation of concentration transport equation. Direct forcing IB method is employed to treat solid object bumps in the fluid flow. The incompressible Navier-Stokes solutions are obtained through the projection method. Analysis of the smoothing procedure, grid sensitivity and the effect of the Schmidt numbers is performed for the turbidity current problem to validate the proposed numerical algorithm, which is shown to be capable of accurately demonstrating their results. Finally, several problems of turbidity current over a three-dimensional seafloor are investigated. The front locations of the currents interacting with the bump are predicted under different Reynolds numbers. Also, the current properties, namely the suspended particle mass, sedimentation rate and energy budget, are compared with the available numerical results.