  We investigate the equation of state(EoS) and the effect of the hadron-quark
phase transition of strong interaction matter in compact stars. The hadron
matter is described with the relativistic mean field theory,and the quark
matter is described with the Dyson-Schwinger equation approach of QCD. The
complete EoS of the hybrid star matter is constructed with not only the Gibbs
construction but also the 3-window interpolation. The mass-radius relation of
hybrid stars is also investigated. We find that, although the EoSs of both the
hadron matter with hyperon and $\Delta$-baryon and the quark matter are
generally softer than that of the nucleon matter, the 3-window interpolation
construction may provide an EoS stiff enough for a hybrid star with mass
exceeding 2$M_{\odot}^{}$ and, in turn, solve the so called "hyperon puzzle".
