On the assumption that the frequencies of the inductor current and output voltage are much lower than the switching frequency of the converter, the critical condition between the discontinuous conduction mode (DCM) and the continuous conduction mode (CCM) is given, and the transfer function of the closed loop output to the reference voltage under DCM and CCM are derived respectively. The analytical results show that the DC-DC Boost converter can be stable in the state of period 1 in DCM, but it can not be stable in CCM, i.e., the low-frequency oscillation will occur. Further, the frequency of the low-frequency oscillation is calculated by using zero-pole analysis method, and the oscillation amplitude of the output voltage is calculated in terms of the topology of the circuit. Finally, the theoretical results are verified by numerical simulations and circuit experiments.