This paper presents an adaptive sliding model controller for rapid earth fault current limiters (REFCLs) in resonant grounded power distribution networks to mitigate the impacts of powerline bushfires by compensating the fault current along with the faulty phase voltage. The powerline bushfire mitigation application using REFCLs with residual current compensation (RCC) inverters requires extremely fast response from the controller used for these inverters. The proposed adaptive sliding mode controller is designed based on the global terminal sliding surface (GTSS) in conjunction with a quick reaching law in order to achieve the fast compensation of the fault current and faulty phase voltage. Furthermore, a parameter adaptation law is used to estimate the parameter of the arc suppression coil used within REFCLs so that the controller provides robustness against parametric uncertainties. Rigorous simulations are carried out on a test distribution system to justify the effectiveness this newly proposed adaptive sliding mode controller in terms of eliminating the fault current and faulty phase voltage so that the impacts of powerline bushfires are minimized. Simulation results are also compared with an integral sliding mode controller in order to demonstrate the effectiveness of the adaptive sliding mode controller in terms of maintaining the performance guideline for mitigating powerline bushfires.