Diffusion is an important mass transport mechanism in ultra-low permeability shale matrix and thus, characterization of shale diffusivity is of practical necessity for shale gas developments. We present a novel method for measuring bulk and local diffusion coefficients of shale core-plugs using dynamic Xray micro-computed tomography (micro-CT). Liquid diffusion experiments are conducted on a centimeter-scale shale core and a series of time-sequenced 3D micro-CT images are acquired through dynamic imaging. Local diffusion coefficients are measured numerically from the micro-CT data using a new mathematical method that allows us to evaluate the heterogeneity of shale diffusivity at the sub-core scale. The variation of local diffusion coefficients is quantified using the Dykstra Parsons method, which provides a means to quantify core-scale heterogeneity in shale samples. Although the micro-CT image data may be influenced by noise, the presented technique provides reasonable results and our validation studies provide fundamental design parameters for measuring diffusivity values from dynamic micro-CT experiments. In addition the presented method can be applied to other porous materials where diffusion occurs. (C) 2017 Elsevier Ltd. All rights reserved.