In aerial load transportation applications, knowing the mass of the load in advance is not always possible. The load dynamics depend on its mass and using a high-performance model-based controller with an inaccurate mass will introduce unmodeled disturbances to the system that will negatively affect the closed-loop performance. This paper addresses the design of a trajectory tracking controller for a quadrotor with a slung-load that has an unknown mass. The proposed solution is an adaptive controller with online estimation designed using the backstepping technique. Nonlinear control laws for thrust and angular velocity, and an adaption law for mass estimation are proposed, which guarantee the convergence of the trajectory tracking and the estimation errors to zero, and are robust to variations in load mass. Simulation and experimental results are presented to assess the validity and performance of the proposed controller.