Mineral mapping identifies minerals distributed in a specific geographic area and plays a significant role in several fields and industries, such as mining, environmental monitoring, land management, and space exploration. Hyperspectral imaging is a fast-developing technique for mineral mapping due to its outstanding discriminating ability with a wide range of spectral bands with high spectral resolution. This paper aims to effectively and accurately map the mineral distribution at Cuprite, Nevada using the new Prisma hyperspectral imagery and novel Bayesian convolutional unmixing network algorithm modeling the endmember variability and spatial correlation. Comparative results show that our proposed method outperforms both classification-based algorithms and traditional spectral unmixing approach given limited training samples.