Border collision bifurcations have received much attention in recent years. A class of piecewise smooth maps with two border and three zones is derived to describe the dynamics of a current-programmed Buck converter operating in a discontinuous mode. The numerical simulation is carried out and the bifurcation diagrams with the reference current as a parameter are obtained. Then, a concrete analysis of the stable existence condition of the fixed point is made, and the structure of bifurcation diagrams and a change in operation mode of the converter at the border collision point are studied. Finally, simulation and experimental results show that the theoretical analysis is correct.