As is well-known that the general radiation hydrodynamics models include two main coupled parts: one is macroscopic fluid part,which is governed by the compressible Navier-Stokes-Fourier equations; the other is radiation field part,which is described by the transport equation of photons.Under the two physical approximations: "gray" approximation and P1 approximation,one can derive the so-called Navier-Stokes-Fourier-P1 approximation radiation hydrodynamics model from the general one.In this paper we study the nonrelativistic limit problem for the Navier-Stokes-Fourier-P1 approximation model due to the fact that speed of the light is much larger than the speed of the macroscopic fluid.Our results give a rigorous derivation of the widely used macroscopic model in radiation hydrodynamics.