We present a trajectory tracking controller for the full dynamics of a quadrotor vehicle carrying a slung load attached by a string. The full dynamic system is modeled as two connected subsystems, the string-load subsystem, with dynamics identical to that of a standard quadrotor in free flight, and the quadrotor subsystem with attitude kinematics and dynamics. A trajectory tracking controller for the position of the point-mass load is designed based on existing Lyapunov-based trajectory tracking controllers for free flying quadrotors which are further backstepped through the quadrotor attitude dynamics. A parameterized Lyapunov function is provided for the full system dynamics with a negative semi-definite time derivative. The proposed controller is proven to drive the load position error to zero and the origin of the error system is exponentially stable. Simulation results attest the performance of the proposed controller for aggressive trajectories and its robustness and validity are further highlighted by experimental results with a model-scale vehicle and slung load. (C) 2019 Elsevier Ltd. All rights reserved.