A Hyperspectral (HS) image provides observational powers beyond human vision capability but represents more than 100 times data compared to a traditional image. To transmit and store the huge volume of a HS image, we argue that a fundamental shift is required from the existing 'original pixel intensity'-based coding approaches using traditional image coders (e.g. JPEG2000) to the 'residual' based approaches using a video coder for better compression performance. A modified video coder is required to exploit spatial-spectral redundancy using pixel-level reflectance modelling due to the different characteristics of HS images in their spectral and shape domain of panchromatic imagery, compared to traditional videos. In this paper a novel coding framework using Reflectance Prediction Modelling (RPM) in the latest video coding standard High Efficiency Video Coding (HEVC) for HS images is proposed. A HS image presents a wealth of data where every pixel is considered as a vector for different spectral bands. By quantitative comparison and analysis of pixel vector's distribution along spectral bands, we conclude that modelling can predict the distribution and correlation of the pixel vectors for different bands. To exploit distribution of the known pixel vector, we estimate a predicted current spectral band from the previous bands using Gaussian mixture-based modelling. The predicted band is used as the additional reference band together with the immediate previous band when we apply the HEVC. Every spectral band of a HS image is treated like it is an individual frame of a video. In this paper, we compare the proposed method with mainstream encoders. The experimental results are fully justified by three types of HS dataset with different wavelength ranges. The proposed method outperforms the existing mainstream HS encoders in terms of rate-distortion performance of HS image compression.