Abstract: One source blind extraction can be used to blind beamfonning for underwater acoustic arrays. Among existing candidate approaches such as the simple constant modulus Algorithm (CMA), Kurtosis Maximization Algorithm (KMA), etc., KMA can separate both negative and positive kurtosis signals. As KMA is used to separate underwater acoustic signals the convergence rate is low. Present paper applies logarithm of kurtosis to form tho objective function, and proposes a one source blind extraction algorithm based on logaritlnii-kiiirtosis maximization. At the same time, double deflation algorithms are also proposed to separate more signals in turn. In contrast to KMA convergence rate is improved. A nonlinear Function is used in learning so that the algorithm can choose the learning step automatically. Computer simulations verify the proposed algorithm.