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The detection of small targets within the background of sea clutter is a significant challenge faced in radar signal processing. Small target echoes are weak in energy, and can be submerged by sea clutter and sea spikes, which are caused by overturning waves and breaking waves. This severely affects the radar target detection performance. This paper proposes a smoothed pseudo-Wigner–Ville distribution–singular value decomposition (SPWVD-SVD) method for sea clutter suppression. This method determines the instantaneous frequency range of the target by contrasting the time–frequency characteristics of the sea spike and the target. Subsequently, it employs a singular value difference spectrum to reduce the rank of the Hankel matrix, thereby reducing the computational burden of the instantaneous frequency estimation step in the experiment. Based on the instantaneous frequency range of the target in the time–frequency domain, the singular values of the target signal are retained, while the singular values of clutter are set to zero. This process accomplishes the reconstruction of radar echo signals and effectively achieves the suppression of sea clutter. The suppression effect is verified using simulation data alongside ten sets of Intelligent Pixel processing X-band (IPIX) radar data against the background of sea spikes. By contrasting the clutter amplitudes before and after suppression, the SPWVD-SVD algorithm demonstrated an average clutter suppression of 15.06 dB, which proves the effectiveness of the proposed algorithm in suppressing sea clutter.