A class of piecewise smooth maps with three zones is derived to describe the dynamics of a current-programmed Buck-Boost converter operating in a discontinuous mode. The numerical simulation is carried out and the bifurcation diagrams w ith the input voltage as a parameter are obtained. It is shown that, when a bifu rcation occurs, some eigenvalues of the Jacobian matrix jumps over the unit circ le in a discontinuous way, and there are always some orbit points lying on the b oundaries which separate different regions in the phase plane. It is concluded t hat border collision bifurcations could occur when the input voltage varies, for example, a bifurcation from a periodic orbit to another periodic orbit or chaot ic orbit.