  Neutron star due to their high interior matter density are expected to be
composed of a quark core, a mixed quark-hadron matter, and a layer of hadronic
matter. Thus, in this paper, we compute the equation of state of these parts of
neutron star to evaluate its structure properties. We use two models for
describing EOS of quark matter, NJL and MIT bag models, and employ three
approaches in this work. A density dependent bag constant satisfy the quark
confinement in the simple MIT bag model. We also study the interaction behavior
of quarks, firstly one gluon exchange within MIT bag model and the secondly
dynamical mass will be held as effective interaction that roles between
particles. Density dependence of quark mass is obtained from NJL self
consistent model. NJL model is a effective manner for justify the chiral
symmetry. Applying the Gibbs conditions the equation of state of the quarks and
hadrons mixed phase is obtained. Since the hadronic matter is under the
influence of strong force of nucleons, we calculate the equation of state of
this phase using a powerful variational many-body technique. Finally, we
calculate the mass and radius of a cold neutron star with a quark core by
numerically solving the TOV equation. To check our used EOS, we compare our
results with the recent observational data. Our results are in a good agreement
with some observed compact objects such as $SAXJ1748.9-2021$, $4U1608-52$ and
$Vela X-1$.
