For over-the-horizon (OTH) radar, the ocean clutter is very strong. And this becomes a big challenge for the target detection. The clutter suppression is a very important procedure for the OTH radar. For the skywave OTH radar, the radar signal will propagate through the ionosphere. This will cause a contamination due to its unstable movement. Then the Bragg frequencies will be smeared and clutter spectrum will spread wider rather than a single line spectra. This smear will cause the target more difficult to be detected and even buried in clutter. Compensation is necessary to cancel the ionospheric effect. This article proposes the clutter decontamination algorithm based on the complex energy detector (CED). The energy detector (ED) is originally proposed to demodulate the real AM-FM signals. The ED is expanded to complex domain. After the expansion, there is no mutual coupling between the amplitude and frequency component for an AM-FM signal. The phase of the Bragg clutter return contaminated by the ionosphere is modeled by a frequency-modulated signal, while its magnitude is amplitude modulated. The CED algorithm is applied to track the instantaneous frequency of the contaminated return signal, which is then used for compensation. Simulation results are presented. The simulation results show that, comparing with the Hankel rank reduction algorithm, the proposed algorithm has better performance under the situation of large frequency fluctuation.