It has been recognized that videos have to be encoded in a rate-distortion optimized manner for high coding performance. Therefore, operational coding methods have been developed for conventional distortion metrics such as Sum of Squared Error (SSE). Nowadays, with the rapid development of machine learning, the state-of-the-art learning based metric Video Multimethod Assessment Fusion (VMAF) has been proven to outperform conventional ones in terms of the correlation with human perception, and thus deserves integration into the coding framework. However, unlike conventional metrics, VMAF has no specific computational formulas and may be frequently updated by new training data, which invalidates the existing coding methods and makes it highly desired to develop a rate-distortion optimized method for VMAF. Moreover, VMAF is designed to operate at the frame level, which leads to further difficulties in its application to today’s block based coding. In this paper, we propose a VMAF oriented perceptual coding method based on piecewise metric coupling. Firstly, we explore the correlation between VMAF and SSE in the neighborhood of a benchmark distortion. Then a rate-distortion optimization model is formulated based on the correlation, and an optimized block based coding method is presented for VMAF. Experimental results show that 3.61% and 2.67% bit saving on average can be achieved for VMAF under the low_delay_p and the random_access_main configurations of HEVC coding respectively.