In order to predict bifurcation point of the closed-loop current-programmed boost converter and enable this converter to operate at stable parameter space, this paper firstly establishes stroboscopic maps for this converter in the continuous conduction mode according to operating characteristics and topple of this converter. Parameter space at the steady state and bifurcation types are analysed together with stability theory of nonlinear equation. In the solving course, the duty cycle is avoided because of inversive solution, and accuracy is increased. Finally, correction is proved by numerical calculation.