  The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to
include $\Delta$-isobars for the study of dense nuclear matter and neutron
stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2
particle. Both the direct and exchange terms of the $\Delta$-isobars'
self-energies are evaluated in details. In comparison with the relativistic
mean field theory (Hartree approximation), a weaker parameter dependence is
found for DDRHF. An early appearance of $\Delta$-isobars is recognized at
$\rho_B\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that
the $\Delta$-isobars' softening of the equation of state is found to be mainly
due to the reduced Fock contributions from the coupling of the isoscalar
mesons, while the pion contributions are found negligibly small. We finally
conclude that with typical parameter sets, neutron stars with $\Delta$-isobars
in their interiors could be as heavy as the two massive pulsars whose masses
are precisely measured, with slightly smaller radii than normal neutron stars.
