Current mode controlled Boost converter has two boundaries in a wide range of circuit parameters. This paper establishes the piecewise smooth iterative map of the converter by utilizing ramp compensation current and derives borderline equations of the orbit state shifting. The reverse bifurcation diagrams and dynamic behavior distribution diagrams with input voltage and compensation slope as parameters are obtained by numerical simulation. The results indicate that with the input voltage reduction, Boost converter enters into robust chaos under continuous conduction mode （CCM） through a border-collision bifurcation on border 1 from stable period-one, and enters into weak chaos and strong intermittency under discontinuous conduction mode （DCM） via a border-collision bifurcation on border 2 By using ramp compensation, the Boost converter can shift from DCM to CCM, and can effectively be controlled to operate at stable period-one region.