  We construct the equation of state (EOS) in a wide density range for neutron
stars using the relativistic mean field theory. The properties of neutron star
matter with both uniform and non-uniform distributions are studied
consistently. The inclusion of hyperons considerably softens the EOS at high
densities. The Thomas-Fermi approximation is used to describe the non-uniform
matter, which is composed of a lattice of heavy nuclei. The phase transition
from uniform matter to non-uniform matter occurs around $0.06 \rm{fm^{-3}}$,
and the free neutrons drip out of nuclei at about $2.4 \times 10^{-4}\
\rm{fm^{-3}}$. We apply the resulting EOS to investigate the neutron star
properties such as maximum mass and composition of neutron stars.
