The period-doubling bifurcation in DC-DC converters has been investigated widely. However, the studies main focus on the models of bifurcations and the identification of strange attractors, the essential mechanism causing period-doubling bifurcation was not analyzed. This paper deduces mathematically the conditions of producing the period-doubling bifurcation in discontinuous current mode (DCM) Boost and Buck converters based on voltage feedback control. It exposes the mechanism of the period-doubling bifurcation in DC-DC converters and perfects the theoretical analysis method, puting forward an analytic method for studying the period-doubling bifurcation.