The block-matching motion estimation has been aggressively developed for years. Many papers have presented fast block-matching algorithms (FBMAs) for the reduction of computation complexity. Nevertheless, their results, in terms of video quality and bitrate, are rather content-varying. Very few FBMAs can result in stationary or quasi-stationary video quality or bitrate for different types of video content. This paper presents a content-motion-aware motion estimation for quality-stationary video coding. By adaptively specifying the subsample ratio, the proposed algorithm can adjust the computational load for acceptable quality loss under the rate control mechanism. As the simulation result, the proposed algorithm can produce stationary quality at the PSNR of 0.36 dB for a given bitrate while saving about 69.6% power consumption.