Background: The self-consistent Thomas-Fermi approximation has been widely used in atomic and nuclear physics. Many properties of nuclei can be described by the Thomas-Fermi approximation in good agreement with experimental data. Purpose: We studied the non-uniform nuclear matter using the self-consistent Thomas-Fermi approximation with a relativistic mean-field model. Methods: The non-uniform matter was assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. We determined the thermodynamically favored state by minimizing the free energy density with respect to the radius of the Wigner-Seitz cell

while the nucleon distribution in the cell was determined self-consistently in the Thomas-Fermi approximation. Results: A detailed comparison is made between the present results and previous calculations in the Thomas-Fermi approximation with a parameterized nucleon distribution that has been adopted in the widely-used-Shen-EOS (equation of state). Conclusion: It has been found that there is no obvious difference in nucleon distributions at lower densities

while the difference becomes noticeable near the transition density to uniform matter. For thermodynamical quantities

such as the free energy and entropy per baryon

the results of both methods generally agree well with each other. Abstract