  Asymmetric nuclear matter is treated in the formalism of Dirac-Brueckner
approach with Bonn one-boson-exchange nucleon-nucleon interaction. We extract
the symmetry energy coefficient at the saturation to be about 31 MeV, which is
in good agreement with empirical value of $30\pm 4$ MeV. The symmetry energy is
found to increase almost linearly with the density, which differs considerably
from the results of non-relativistic approaches. This finding also supports the
linear parameterization of Prakash, Ainsworth and Lattimer. We find,
furthermore, that the higher-order dependence of the nuclear equation of state
on the asymmetry parameter is unimportant up to densities relevant for neutron
stars. The resulting equation of state of neutron-rich matter is used to
calculate the maximum mass of neutron star, and we find it to be about
2.1$M_\odot$. Possible mechanisms for the softening of the equation of state
are also discussed.
