The electrode of a vanadium redox flow battery generally is a carbon fibre-based porous medium, in which important physicochemical processes occur. In this work, pore-scale simulations are performed to study complex multiphase flow and reactive transport in the electrode by using the lattice Boltzmann method (LBM). Four hundred fibrous electrodes with different fibre diameters and porosities are reconstructed. Both the permeability and diffusivity of the reconstructed electrodes are predicted and compared with empirical relationships in the literature. Reactive surface area of the electrodes is also evaluated and it is found that existing empirical relationship overestimates the reactive surface under lower porosities. Further, a pore-scale electrochemical reaction model is developed to study the effects of fibre diameter and porosity on electrolyte flow, VII/VIII transport, and electrochemical reaction at the electrolyte-fibre surface. Finally, evolution of bubble cluster generated by the side reaction is studied by adopting a LB multiphase flow model. Effects of porosity, fibre diameter, gas saturation and solid surface wettability on average bubble diameter and reduction of reactive surface area due to coverage of bubbles on solid surface are investigated in detail. It is found that gas coverage ratio is always lower than that adopted in the continuum model in the literature. The current pore-scale studies successfully reveal the complex multiphase flow and reactive transport processes in the electrode, and the simulation results can be further upscaled to improve the accuracy of the current continuum-scale models.