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Neutron star due to their high interior matter density are expected to becomposed of a quark core, a mixed quark-hadron matter, and a layer of hadronicmatter. Thus, in this paper, we compute the equation of state of these parts ofneutron star to evaluate its structure properties. We use two models fordescribing EOS of quark matter, NJL and MIT bag models, and employ threeapproaches in this work. A density dependent bag constant satisfy the quarkconfinement in the simple MIT bag model. We also study the interaction behaviorof quarks, firstly one gluon exchange within MIT bag model and the secondlydynamical mass will be held as effective interaction that roles betweenparticles. Density dependence of quark mass is obtained from NJL selfconsistent model. NJL model is a effective manner for justify the chiralsymmetry. Applying the Gibbs conditions the equation of state of the quarks andhadrons mixed phase is obtained. Since the hadronic matter is under theinfluence of strong force of nucleons, we calculate the equation of state ofthis phase using a powerful variational many-body technique. Finally, wecalculate the mass and radius of a cold neutron star with a quark core bynumerically solving the TOV equation. To check our used EOS, we compare ourresults with the recent observational data. Our results are in a good agreementwith some observed compact objects such as $SAXJ1748.9-2021$, $4U1608-52$ and$Vela X-1$.

The structure of cold neutron star with a quark core within the MIT and NJL models