A new technique is proposed for range alignment in Inverse Synthetic Aperture Radar (ISAR). The basic idea is to perform range alignment using a maximum kurtosis (fourth-order central moment) criterion. After maximizing the kurtosis of the combined range profile of two adjacent echoes,the amount of range shift between them can be automatically tracked out. The combined range profile is constructed by a max operation, which only reserves the larger elements of the two echoes, and the echoes amplitudes are limited before they are combined. This algorithm has been used to process real ISAR data and the results demonstrate the effectiveness of the method. Compared with the correlation method and the minimum entropy method, the proposed algorithm obtains much better results in both examples in this paper. Its computation complexity has the same order of magnitude as the minimum entropy method.