Reverberation is the main background interference in underwater active sonar target detection that seriously interferes with the extraction of target echo. In this paper, a signal enhancement algorithm utilizing fractional lower-order moments based on reverberation statistical distribution information is proposed. As fractional lower-order moments can only be applied on symmetric α-stable random variables, energy redistribution method is proposed to make reverberation signal satisfy the symmetric α-stable distribution. To evaluate the proposed algorithm, an experiment involving simulated linear frequency modulation reverberation with the proposed method and comparison methods is performed and discussed. Moreover, an experiment is conducted using reverberation as measured from the lake. The results show that the proposed algorithm can achieve better reverberation suppression and signal enhancement performance compared with other methods.