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An efficient and accurate R-Q model is greatly important for intra-frame rate control of the latest High Efficiency Video Coding (HEVC) standard. However, previous methods pay more attention to the gradient based rate quantization (R-Q) model for the intra-frame rate control. In this paper, we analyze the drawbacks of the gradient based frame complexity measure when applied different Quantization Parameters (QPs). Then we propose a novel edge based frame complexity measure using the Gaussian Gradient operator with properly selected parameters. In order to tackle the problems that the gradient based rate quantization model fails when using the different QPs, we propose an adaptive frame complexity based R-Q model for intra-frame rate control based on these two complexity measures. Simulations have been conducted based on HM6.2 which is the latest reference software of HEVC. Note that we may be the first to do this work, so we do not have the classical methods which have been implemented in HEVC to compare with. In this paper we implement the traditional gradient based and the Cauchy distribution based rate quantization model in HEVC and compare the performance with each other. Here we use bit rate mismatch ratio as the evaluation method. The simulation results show that by using our proposed scheme, up to 33.1% mismatch ratio reduction compared with the Cauchy distribution based model and up to 13% mismatch ratio reduction compared with the gradient based model for intra frames can be achieved.