Sequential Inverse Synthetic Aperture Radar （ISAR） refers to that the radar continuously observing a non-cooperative maneuvering targets during a long period and generating a sequence of ISAR images nearly real time. According to these image sequences， the scattering information and motion state change information of the target can be fully extracted， which is very helpful for target monitoring， tracking and identification. Sequential ISAR imaging of maneuvering targets often requires fine phase compensation. Using the classical algorithm to compensate the phase for each frame individually is computationally intensive and takes a long time to process. In practice， the interval between two adjacent frames of the sequential ISAR is short and the change of the target's motion state is small. In this paper， a new algorithm for sequential ISAR imaging of maneuvering targets is proposed by making full use of the continuity of target motion between adjacent frames and combining Fractional Fourier Transform （FrFT） and Kalman filtering techniques. The algorithm performed FrFT on the azimuthal signal， and achieved the measurement of Azimuthal Chirp Rate （ACR） by searching for the best energy aggregation of FrFT corresponding to the rotation angle. The optimal estimate of the ACR is then obtained using Kalman filtering to achieve accurate phase compensation of the azimuthal signal. The optimal estimate of ACR based on the Kalman filtering of the current frame can reduce the search range of the FrFT rotation angle in the next frame and improve the computational efficiency. The effectiveness of the proposed algorithm is verified by real radar experiment. Compared with the classical FrFT parameter estimation algorithm and PGA algorithm， the proposed algorithm has excellent efficiency and can realize sequential ISAR imaging with better focusing effect.