  In this paper, we use the equation of state based on a modification of 2+1
flavors Nambu-Jona- Lasinio (NJL) model to study the quark matter of hybrid
stars. For comparison, we utilize five EOSs of the relativistic mean-field
(RMF) model to describe the hadronic phase. With the 3- window crossover
interpolation approach, we try to construct relatively soft hybrid EOSs but
find the maximum masses of hybrid stars do not differ too much. The results are
quite close to two solar mass, which is consistent with the mass constraint of
PSR J0348+0432. Furthermore it is noteworthy that the heaviest stable stars
have central densities higher than that of the deconfinement transition thus
suggesting a pure quark core in the hybrid star.
