In this paper, the spinless Fermi systems with arbitrary band filling have been studied by using the real-space renormalization group methods. For one dimensional case, we obtained the ground state energies, the correlation functions and the relative critical exponents of the systems. The results were compared with those of isotropic s = 1/2 X-Y model. We also discussed qualitatively the correlation fuactions and the related critical exponents for the cases of D>1.