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Attention has been focused on the moving target detection in heavy sea clutter. On the basis of detection model of moving target with fluctuant amplitudes, a novel adaptive algorithm in fractional Fourier transform (FRFT) domain is proposed, which combines statistic-based and FRFT-based detection method. FRFT has good energy concentration property on linear frequency modulation (LFM) signal with the optimal transform angle, which is determined by calculating spectral kurtosis (SK) in FRFT domain. Grading iterative search method is used for good accuracy of parameter estimation and fast calculation speed. A novel adaptive line enhancer (ALE) in FRFT domain is proposed to suppress sea clutter and improve signal-to-clutter ratio (SCR), which provides less error and faster convergence. Leakage factor is introduced into the update equation of weight vector to reduce `memory effect` and step size is normalised by the power of input signal with better convergence characteristic. In the end, both X-band and S-band real sea clutter is used for verification and the results present that the proposed algorithm has good convergence property and small mean square error (MSE). Weak moving target in low SCR environment (SCR = -6 dB) can be well detected and estimated, which indicates the effectiveness of the algorithm.