The new generation video standard, i.e., High-efficiency Video Coding (HEVC), shows a significantly improved efficiency relative to the last standard, i.e., H.264. However, the quad tree structured coding units (CUs), which are adopted in HEVC to improve compression efficiency, cause high computational complexity. In this study, a novel fast algorithm is proposed for CU partition in intra coding to reduce the computational complexity. A rough minimum depth prediction of the largest CU method and an early termination method for CU partition based on the total coding bits of the current CU are employed. Many approaches have been proposed to reduce the encoding complexity of HEVC, but these methods do not use the total coding bits of the current CU as the main basis for judgment to judge the CU complexity. Compared with the reference software HM16.6, the proposed algorithm reduces encoding time by 45% on average and achieves an approximately 1.1% increase in Bjntegaard delta bit rate and a negligible peak signal-to-noise ratio loss.