In this paper, a novel adaptive control approach for Unmanned Aerial Manipulators (UAMs) is proposed. The UAMs are a new configuration of the Unmanned Arial Vehicles (UAVs) which are characterized by several inhered nonlinearities, uncertainties and coupling. The studied UAM is a Quadrotor endowed with two degrees of freedom robotic arm. The main objectives of our contribution are to achieve both a tracking error convergence by avoiding any singularity problem and also the chattering amplitude attenuation in the presence of perturbations. Therefore, the proposed Adaptive Nonsingular Terminal Super-Twisting controller (ANTSTW) consists of the hybridization of a Nonsingular Terminal Sliding Mode Control and an Adaptive Super Twisting. The adaptive law, which adjust the Super-Twisting’s parameters, is obtained by using stability Lyapunov theorem. Simulation experiments in trajectory tracking mode were realized and compared with Nonsingular Terminal Super-twisting control to prove the superiority and the effectiveness of the proposed approach.