To solve the problem of that although Intra String Copy (ISC) improved the effect of the screen content coding, but it transformed the 2D image to 1D by Coding Unit (CU), making adjacent regions in an image segmented and spatial correlation not to be used, a new algorithm called 2D Intra String Copy (2D ISC) was proposed. Almost without additional memory in encoder and decoder, the algorithm realized arbitrary 2D shape searching and matching without boundary restriction of CU for pixels in current CU, by using dictionary coding tool in High Efficiency Video Coding (HEVC) reconstruction cache. Also adopted technologies of color quantization preprocessing and horizontal vertical search order self-adaption to enhance coding effect. Experiments on common test for typical screen content test sequences show that compared with HEVC, 2D ISC can achieve bit-rate saving of 46.5%, 34.8%, 25.4% for All Intra(AI), Random Access(RA) and Low-delay B(LB) configurations respectively in lossless coding mode, and 34.0%, 37.2%, 23.9% for AI, RA and LB configurations respectively in lossy coding mode. Even compared with ISC, 2D ISC can also achieve bit-rate saving up to 18.3%, 13.9%, 11.0% for AI, RA and LB configurations in lossless coding mode, and 19.8%, 20.5%, 10.4% for AI, RA and LB configurations in lossy coding mode. The experimental results indicate that the proposed algorithm is feasible and efficient.