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Sea clutter is a kind of ubiquitous interference in sea-detecting radars, which will definitely influence target detection. An accurate sea clutter prediction method is supposed to be beneficial while existing prediction methods are based on the one-step-ahead prediction. In this paper, a sea clutter prediction network (SCPNet) is proposed to achieve the k-step-ahead prediction based on the characteristics of sea clutter. The SCPNet takes a sequence-to-sequence (Seq2Seq) structure as the backbone, and a simple self-attention module is employed to enhance the ability of adaptive feature selections. The SCPNet takes the normalized amplitudes of sea clutter as inputs and is capable of predicting an output sequence with a length of k; the phase space reconstruction theory is also used to find the optimized input length of the sea clutter sequence. Results with the sea-detecting radar data-sharing program (SDRDSP) database show the mean square error of the proposed method is 1.48 × 10−5 and 8.76 × 10−3 in the one-step-ahead prediction and the eight-step-ahead prediction, respectively. Compared with four existing methods, the proposed method achieves the best prediction performance. [ABSTRACT FROM AUTHOR]