Abstract: According to the theory of the fractional lower order statistical signal processing and the characteristics of ship radiated noises, this paper proposes a new noise model of underwater acoustic signals. The reasons of performance degenerate are analyzed for traditional LMS approach. A new replace approach is advanced to adaptive filtering based on fractional lower order moments for underwater acoustic signals. It is analyzed how to affect the performance of LMP algorithm for choosing p value. Theoretic analysis and computer simulations indicate that the new method is not only suitable for Gaussian noise conditions, but also very robust under the lower order -stable distribution noise conditions.