Using random projection acceleration technology to project the Singular Value Decomposition (SVD) of higher dimensional matrices onto a lower subspace can reduce the time consumption of SVD. The singular value random projection compression operator was defined to replace the singular value compression operator, then it was used to improve the Fixed Point Continuation (FPC) algorithm and got FPCrp algorithm. Lots of experiments were conducted on the original algorithm and the improved one. The results show that the random projection technology can reduce more than 50% time consumption of the FPC algorithm, while maintaining its robustness and precision. The modified matrix completion algorithm based on random projection technology is effective in solving large scale problems.