  The properties of neutron stars are investigated by including $\delta$ meson
field in the Lagrangian density of modified quark-meson coupling model. The
$\Sigma^-$ population with $\delta$ meson is larger than that without $\delta$
meson at the beginning, but it becomes smaller than that without $\delta$ meson
as the appearance of $\Xi^-$. The $\delta$ meson has opposite effects on
hadronic matter with or without hyperons: it softens the EOSes of hadronic
matter with hyperons, while it stiffens the EOSes of pure nucleonic matter.
Furthermore, the leptons and the hyperons have the similar influence on
$\delta$ meson effects. The $\delta$ meson increases the maximum masses of
neutron stars. The influence of $(\sigma^*,\phi)$ on the $\delta$ meson effects
are also investigated.
