Accurate translational motion compensation (TMC) is the key procedure of inverse synthetic aperture radar (ISAR) imaging. Under the condition of sparse aperture, the correlation of adjacent pulses is severely destroyed, which brings a few challenges to TMC and imaging. Thus, this paper proposes a novel TMC method for ISAR imaging. In this technique, the signal model of joint phase adjustment and ISAR imaging is established first. Then, the process of TMC is designed. That is, after range alignment with improved global minimum entropy (IGME), the range joint fast orthogonal matching pursuit (RJFOMP) algorithm is applied to ISAR imaging, and the minimum entropy method (MEM) is adopted to estimate the phase error. Meanwhile, the joint optimization of phase adjustment and ISAR imaging is realized through the cyclic iteration. Extensive experiments based on both simulated and measured data demonstrate that the proposed TMC method is effective for two modes of motion errors, which are named as coherent mode (CM) and non-coherent mode (NCM), respectively. When RJFOMP is used for joint phase adjustment and ISAR imaging, it has excellent imaging performance under noisy and sparse conditions.