We are concerned in this paper with the non-relativistic global limits of the entropy solutions to the Cauchy problem of 3×3 system of relativistic Euler equations modeling the conservation of baryon numbers, momentum, and energy respectively. Based on the detailed geometric properties of nonlinear wave curves in the phase space and the Glimm’s method, we obtain, for the isothermal flow, the convergence of the entropy solutions to the solutions of the corresponding classical non-relativistic Euler equations as the speed of light c → +∞.