The Doppler frequency time-variation exist in the received echo when imaging maneuvering targets by Inverse Synthetic Aperture Laser radar (ISAL). Based on a keystone transform in the azimuth time-frequency domain, a fast azimuth imaging algorithm of ISAL for maneuvering targets is proposed. Since the ratio of the chirp rate to the initial frequency is constant for all multicomponent linear frequency modulation subechoes in each range cell, all these multicomponent linear frequency modulation subechoes can be simultaneously transformed into multi-component single frequency subechoes by using the keystone transform in the azimuth time-frequency domain, and hence fast Fourier transform can be used for azimuth focusing. In addition, a precise and efficient method based on the fractional Fourier transform and the minimum entropy is proposed to estimate the ratio of the chirp rate to the initial frequency. Simulation results prove that, comparing with the range-instantaneous Doppler algorithm based on the Radon-Wigner transform, the proposed algorithm is more efficient and can preserve more information details of the target.