The two-phase flow is a kind of dissipative structure in multiphase hydrodynamics. A drift-flux model with four equations is adopted to investigate the natural circulation bifurcation, in which the sub-cooled boiling, condensation, and void fraction etc. have been taken into occount. The bifurcation spectrum of a natural circulation system with low steam quality and low system pressure is presented and the physical mechanisms of bifurcation are described in detail. Bifurcation characteristics of the two-phase natural circulation indicate typical static instability observed in HRTL-5 simulating the geometry and system design of the 5MW nuclear heating reactor operating at low steam quality and low system pressure. Analysis shows: (1) bifurcation phemomenon can occur in a two-phase natural circulation under certain thermal and geometrical condition; (2) with changing, namely increasing and decreasing, control parameters, the tracks of the work points of the natural circulation system are not identical, which shows the basic characteristic of the bifurcation phemomenon; (3) the bifurcation phenomenon of the natural circulation delay and disappear with increasing system pressure and decreasing heat flux.