The quadrotor aerial robot is a complex system and its dynamics involve nonlinearity, uncertainty, and coupling. In this paper, an adaptive backstepping sliding mode control (ABSMC) is presented for stabilizing, tracking, and position control of a quadrotor aerial robot subjected to external disturbances. The developed control structure integrates a backstepping and a sliding mode control approach. A sliding surface is introduced in a Lyapunov function of backstepping design in order to further improve robustness of the system. To attenuate a chattering problem, a saturation function is used to replace a discontinuous sign function. Moreover, to avoid a necessity for knowledge of a bound of external disturbance, an online adaptation law is derived. Particle swarm optimization (PSO) algorithm has been adopted to find parameters of the controller. Simulations using a dynamic model of a six degrees of freedom (DOF) quadrotor aerial robot show the effectiveness of the approach in performing stabilization and position control even in the presence of external disturbances.