Abstract: The fourth-order cumulant of Gaussian distribution zero-mean noise has always been zero theoretically, yet the probability density of real noise and reverberation remains to be a key problem to performance of the fourthorder cumulant beam forming technique. In the present paper, aiming at the instantaneous amplitude distribution of the ambient sea noise and bottom reberberation, we, respectively, deduce the fourth-order cumulant beam forming array gain function; establish the relations between array gain and number of the array elements, ambient sea noise, fourth-order and second-order statistical property of the bottom reverberation as well as input signal-to-noise ratio; also confirm that, compared with conventional beam-forming with critical signal-to-noise ratio and super-critical signal-tointerference ratio, the fourth-order cumulant beam forming could obtain higher gain and better distinguishability than the conventional beam-forming. The results of experiment data processing demonstrate the consistency between theory and consequence of gain and distinguishability of the fourth-order cumulant beam forming.