The processing unit with a quad-tree structure in high efficiency video coding (HEVC/H.265) consists of a coding unit (CU), a prediction unit (PU), and a transform unit (TU). The CU and PU account for the majority of the computational complexity. This paper proposes a fast inter-prediction algorithm to overcome the high-computational demand associated with the coding complexity for an HEVC/H.265 encoder. In this paper, the CU depth prediction is proposed to reduce the number of CU executions by incorporating the depths and rate-distortion costs (RD-costs) of the adjacent CUs. Bimodal RD-cost segmentation is proposed for the elementary dichotomy of RD-cost distribution. The proposed algorithm applies the one-sided Chebyshev's inequality for the determination of accurate RD-cost thresholds by adjusting the error rates for early termination and early split. Our approach achieves 50.1% and 48.7% time savings with Bjøntegaard delta bit rate (BDBR) increases of 1.2% and 1.0% compared to the HEVC/H.265 reference software for random access and low delay configurations, respectively. The proposed method has better performance than earlier researches in terms of both coding speed and rate-distortion.