  With the equations of state provided by the newly developed density dependent
relativistic Hartree-Fock (DDRHF) theory for hadronic matter, the properties of
the static and $\beta$-equilibrium neutron stars without hyperons are studied
for the first time, and compared to the predictions of the relativistic mean
field (RMF) models and recent observational data. The influences of Fock terms
on properties of asymmetric nuclear matter at high densities are discussed in
details. Because of the significant contributions from the $\sigma$- and
$\omega$-exchange terms to the symmetry energy, large proton fractions in
neutron stars are predicted by the DDRHF calculations, which strongly affect
the cooling process of the star. The critical mass about 1.45 $M_\odot$, close
to the limit 1.5 $M_\odot$ determined by the modern soft X-ray data analysis,
is obtained by DDRHF with the effective interactions PKO2 and PKO3 for the
occurrence of direct Urca process in neutron stars. The maximum masses of
neutron stars given by the DDRHF calculations lie between 2.45 M$_\odot$ and
2.49 M$_\odot$, which are in reasonable agreement with high pulsar mass $2.08
\pm 0.19 M_\odot$ from PSR B1516+02B. It is also found that the mass-radius
relations of neutron stars determined by DDRHF are consistent with the
observational data from thermal radiation measurement in the isolated neutron
star RX J1856, QPOs frequency limits in LMXBs 4U 0614+09 and 4U 1636-536, and
redshift determined in LMXBs EXO 0748-676.
