We study the inner structure of a neutron star from a theoretical point of view and the outcome results are compared with observed data. We propose a stiff equation of state relating pressure with matter density. From our study we calculate mass (M),compactness (u) and surface redshift (Zs) for two binary millisecond pulsars, namely PSR J1614-2230 and PSR J1903+327, and four X-ray binaries, namely Cen X-3, SMC X-1, Vela X-1 and Her X-1,and compare them with recent observational data. Finally, we examine the stability for such a type of theoretical structure.