This work deals with the numerical approximation of the Homogeneous Relaxation Model (HRM) which is a mixture model widely used for simulating two-phase flows. This four-equations model is derived from the six-equation two-fluid model. In order to numerically solve the HRM system, we use a classical finite volume approach as described in [4] and the Roe solver [3] for the approximation of the convective fluxes on each face of the mesh. As explained in [2], this type of scheme suffers from an accuracy problem in the low Mach number limit on 2D and 3D cartesian grids. A pressure correction applied to the numerical momentum flux enables to recover the right order of accuracy. However, by removing some spatial diffusion, checkerboard modes can appear and also be amplified by discontinuous source terms . In order to get rid of these checkerboard modes, we want to extend the new corrected Roe scheme detailed in [1] to the resolution of the two-phase flow HRM system.