Sliding mode control (SMC) is known as a robust control method to maintain system performance and keep it insensitive to system uncertainties. To achieve this objective, the knowledge of the uncertainty bound is usually needed, but sometimes it could be a hard task. Hence, the adaptive technology is introduced to be synthesized with SMC. In this paper, a novel adaptive SMC (ASMC) scheme is proposed to accommodate system uncertainties caused by actuator faults. An integral sliding mode controller is used as the baseline controller. When actuator faults occur, there is no need to know the exact bound of the uncertainties in control effectiveness matrix. The post-fault control effectiveness matrix can be estimated by the proposed adaptive control scheme, and the control inputs will be changed accordingly. In such a way, the robustness of the controller to actuator faults is improved. With the help of adaptive change of both continuous and discontinuous control parts, a minimum value of the discontinuous control gain can be guaranteed. In this case, the resulting control effort is reduced accordingly to avoid control chattering effect. Owing to the minimized control effort to accommodate uncertainties compared to the conventional SMC, the proposed ASMC can still maintain the system performance when severer faults occur. The effectiveness of the developed algorithm is demonstrated by the simulation results based on an unmanned quadrotor helicopter under various faulty conditions.