Without the turbulence of atmosphere, spaceborne inverse synthetic aperture lidar (ISAL) can obtain high-resolution images of orbit objects at a long distance. Therefore, ISAL plays an important role in spaceborne imaging. The cross-range echo signal model of spaceborne ISAL is established. Generally, the motion of an orbital object is considered a second-order rotation after translational compensation, i.e. uniformly accelerated rotation. Under this condition, the ISAL cross-range echo signals can be equivalent to multicomponent linear frequency modulation (LFM) signals with various chirp rate and initial frequency. Therefore, it is difficult to obtain a well-focused image when using the traditional FFT method. A fast cross-range imaging algorithm based on Radon-Wigner transform is proposed. The Radon-Wigner transform combined with a successive elimination procedure are performed to estimate and separate the cross-range multicomponent LFM signals one by one from strong to weak, in each range unit. After prominent peak points are estimated and extracted in all range units, rearrangement is performed by linear superposition and a focused 2D ISAL image can be obtained. The proposed method avoids to obtain signal parameters and conduct instantaneous Doppler imaging, which is simplified and greatly improved in efficiency. Simulation results show that, compared with the traditional range instantaneous Doppler imaging algorithm, the average processing time of the proposed algorithm is reduced from 222.66 s to 23.51 s. In the case of low signal-to-noise ratio, the target contour in the image is more significant and easier to detect and recognize.