Our objective is to predict the Fluid-Resonant Oscillation at low Mach number numerically. Because the compressible flow equations become stiff in low-Mach-number flows, we derive a new equation set that is suited for the simulation of such flows under assumption that the compressibility effect is weak. The derived equations are essentially the same as the incompressible Navier-Stokes equations except for an additional term. So we can apply almost the same numerical procedure as developed for the incompressible flow equations. Using the present method, a numerical analysis of flows over a three-dimensional open cavity is performed. The results show that strong pressure fluctuations occur at specific flow velocities. Also shown is that the frequency of the pressure fluctuations is locked-in at the Helmholtz resonant frequency of the cavity. Thus, it is confirmed that the present method is able to predict the Fluid-Resonant Oscillation in low-Mach-number flows.