We have constructed a method (governing equation set and numerical procedure) that is suited for the numerical simulation of the Fluid-Resonant Oscillation at low Mach number. By using the new equation set, which was derived under the assumption that the compressibility effect is weak, we do not have to worry about the stiffness problem from which we suffer when using the usual compressible flow equations. In addition, because the derived equations are essentially the same as the incompressible Navier-Stokes equations except for an additional term, we can apply almost the same numerical procedure as developed for the incompressible flow equations. In order to verify the present method, we applied it to the flow over a three-dimensional open cavity, where a kind of Fluid-Resonant Oscillation called wind-throb occurs. By comparing the computational results with the experimental data, it is confirmed that the present method has the capability of predicting the Fluid-Resonant Oscillation in low-Mach-number flows. Furthermore, the validity of the present method is also examined for the simulation of the noise-reduction effect of the deflector, which is usually used for the suppression of wind-throb in the cabin of vehicles running with the sunroof or window open.