In this paper we proposed a modified Baer-Nunziato model for compressible multi-fluid flows, with main attention on the energy exchange between the two fluids. The proposed model consists of eleven PDEs; however, the use of the particular phase evolving variables may reduce the model to have only six PDEs. The main advantage of the model is that the Abgrall's UPV criterion on mixture velocity and pressure is satisfied without affecting either its hyperbolicity or its conservations of the two individual masses, momentum or total energy. An Lax-Friedrichs scheme is built for a particular case of the proposed model. When the two fluids in the fluid mixture are both of the linear Mie-Gruneisen type, the scheme satisfies the Abgrall's UPV criterion on mixture velocity and pressure. Numerical experiments with polytropic, barotropic, stiffened and van der Waals fluids show that the scheme is efficient and able to treat fluids characterized with quite different thermodynamics.