Quadrotor UAVs are subject to different technical and operational constraints, thus, it is important to increase its technical reliability in critical areas to ensure a safe flight despite faults. Quadrotor hardware redundancy (in actuators and sensors) has been used extensively in order to solve reliability shortcomings last years but software improvement, especially, that associated to fault tolerant control laws needs more attention and research. This paper leads with the stabilization problem of an under-actuated quadrotor during the occurrence of actuator partial fault. The main idea of the proposed solution is to verify the robustness of a Sliding Mode Control (SMC) based control law called Conditional Integrator SMC (CISMC) in order to stabilize a quadrotor and allow a safe trajectory tracking by controlling quadrotor attitude and position. The effectiveness of the proposed Passive Fault Tolerant Control (PFTC) was tested by numerical simulations in the presence of partial loss of effectiveness (hard-over) of one actuator and compared to classical PID controller. Results demonstrated a better performance of CISMC when compared to PID in the presence of partial faults, with an improvement of at least \(28\%\) of more capacity to withstand failures.