Coal is highly anisotropic and heterogeneous, affecting coal permeability. As permeability is one of the most important reservoir properties for coalbed methane production, it is useful to understand the impact of coal anisotropy and heterogeneity on coal permeability. In this work, anisotropic permeability measurements were performed in the laboratory on three cubic samples from the same coal block from the Bowen Basin, Queensland, Australia. The permeability was measured at a series of gas and confining pressures. Cleat compressibility, a measure of permeability sensitivity to stress, was also calculated from the experimental results. Each sample was then scanned using microscopic X-ray computerised tomography after permeability measurements to study its cleat system. The results show that permeability is strongly anisotropic and heterogeneous among the three samples and is correlated with the cleat system. A permeability model, which incorporates stress, gas pressure and swelling effects, is used to describe the experimental results. At last, numerical simulations were conducted to demonstrate the impact of coal permeability heterogeneity on coalbed methane production.