The one-cycle controlled Boost converter is analyzed by using its averaged model. The results show that the one-cycle controlled Boost converter loses stability via a supercritical Hopf bifurcation, which may jeopardize the performance of the converter. A washout filter is proposed in this paper to suppress the Hopf bifurcation. This method can be easily implemented due to the structure of the one-cycle controlled Boost converter. The averaged model of the washout filter-aided one cycle controlled Boost converter is derived. Two new parameters in the washout filter can be chosen by Routh-Hurwitz stability criterion. The washout filter-aided method is verified by simulation and experiment.