Rigorous non-reflective boundary conditions for the multi-component, chemically non-equilibrium reactive flows with real gas effect were derived with the coupling of the species conservations and the fluid equations. The chemically non-equilibrium sound speed was obtained directly from the matrix decomposition of the conservation equations. It was shown that the sound speed of chemically non-equilibrium flow with real gas effect is different from the frozen sound speed of the mixture. The present derivation of non-reflective boundary condition provides the consistency in the characteristic wave speeds for both numerical algorithms of governing equations and boundary conditions. In the limit of single species, the present result reduces to the previous non-reflective boundary conditions given by Poinsot and Lele. The boundary conditions were tested by the shock wave, acoustic wave, vortex and diffusion and premixed flame propagation involving the detailed chemistry and variable thermal properties. The results showed that improper boundary condition generates reflective waves and high frequency noise in the computation domain. It is demonstrated that the present boundary conditions are robust and allow the acoustic and combustion waves propagating out the boundary without causing wave reflection.