CUP-VISAR system is a new technology that combines Compressed Ultrafast Photography (CUP) with two-dimensional Velocity Interferometer System for Any Reflector (VISAR). To solve the problem that the image reconstruction quality of CUP-VISAR system decreases obviously under the condition of large noise, a compressed ultrafast photography reconstruction method based on iteration-interframe dual prediction is proposed. Using this method, the correlation of inter-frame image data and the correlation of iterations before and after the same frame image are studied. The compressed image reconstruction problem is presented as an iteration-inter frame dual prediction optimization problem based on Kalman prediction and inter-frame prediction, and the Plug-and-Play Generalized Alternating Projection (PnP-GAP) framework is used to solve the optimization problem effectively. Simulation results show that the minimum Peak Signal-to-Noise Ratio (PSNR) and minimum Structure Similarity Index Measure (SSIM) of the proposed method are increased by 3.18-2.11 dB and 20.30%-8.22% under large Gaussian noise conditions. The practical results show that the proposed method can obtain higher definition of fringe image, and the reconstructed line-VISAR (1D-VISAR) fringe movement trend is clearer, which verifies the effectiveness of the algorithm.