To solve the problem that the imaging speed is limited by the reference arm acquisition in remote sensing experiment based on correlated imaging, a repeatable pseudo-thermal light based on random phase plate scanning is proposed. The repeatable laser speckles are produced so that reference arm acquisition is not necessary in imaging process. Repeatability evaluation function is established and the influence of repeatability on image quality are numerically analyzed. Laser intensity jitter and positioning accuracy are pointed out to make sure that the image quality is not affected. The performance of the repeatable pseudo-thermal light is verified, and at the emission velocity of 4000 frames/s, the correlation coefficient can reach more than 0.97 with intensity jitter and positioning accuracy satisfying. The feasibility of the repeatability of pseudo-thermal light is approved and imaging resolution can reach the diffraction limit.