This article deals with the robust finite-time stabilization of a quadrotor subject to perturbations. First, new nonsingular terminal sliding mode variables (NTSMV) are proposed for altitude and attitude that speeds the controlled system’s convergence both before and after it reaches the sliding manifolds of the system. The uniqueness comes in the design of time-varying (TV) sliding surfaces without prior knowledge of the initial system states, resulting in insensitivity to beginning state uncertainty. Then, a robust TV nonsingular terminal sliding mode control scheme is developed based on the results of FTSMV, in which the singularity problem of traditional terminal sliding mode (TSM) control systems is solved by restricting TSM surfaces to non-singular areas. The proposed control strategy applied to the altitude and attitude of a quadrotor guarantees the tracking errors’ finite-time convergence to the origin, as well as the quadrotor overall robustness in the face of enormous uncertainties and unforeseen environmental perturbations. In addition, adaptive tuning laws are designed to estimate the lumped uncertainty’s unknown upper bounds, which is useful in practice, also, the stability of all proposed techniques is proved. All results are illustrated in simulations are compared to others control algorithms.