This study presents an efficient fast bit rate transcoding method for high-efficiency video coding (HEVC) screen content coding (SCC). It utilises the correlation between the current coding unit (CU) and the corresponding decoded CU to skip the normal intra mode or intra block copy mode. Furthermore, quantisation parameter values are also incorporated into the algorithm for better performance. In addition, a fast scheme is designed to skip partial prediction unit modes to accelerate the entire transcoding process. Experimental results show that, compared with the original HEVC SCC reference software (SCM-3.0), the proposed fast intra transcoding algorithms achieve 45.09% transcoding time reduction with only 1.78% Bjotegaard delta bit rate increment for the all-intra case.