The high-efficiency video coding (HEVC) standard improves the coding efficiency at the cost of a significantly more complex encoding process. This is an issue for a large number of video-capable devices that operate on batteries, with limited and varying processing power. A complexity controller enables an encoder to provide the best possible quality at any power quota. This paper proposes a complexity control method for HEVC intra coding, based on a Pareto-efficient rate–distortion–complexity (R–D–C) analysis. The proposed method limits the intra prediction for each block (as opposed to existing methods which limit the block partitioning), on a frame-level basis. This method consists of three steps, namely rate-complexity modeling, complexity allocation, and configuration selection. In the first step, a rate-complexity model is presented which estimates the encoding complexity according to the compression intensity. Then, according to the estimated complexity and target complexity, a complexity budget is allocated to each frame. Finally, an encoding configuration from a set of Pareto-efficient configurations is selected according to the allocated complexity and the video content, which offers the best compression performance. Experimental results indicate that the proposed method can adjust the complexity from 100 to 50%, with a mean error rate of less than 0.1%. The proposed method outperforms many state-of-the-art approaches, in terms of both control accuracy and compression efficiency. The encoding performance loss in terms of BD-rate varies from 0.06 to 3.69%, on average, for 90–60% computational complexity, respectively. The method can also be used for lower than 50% complexity if need be, with a higher BD-rate.