This paper presents the problem of safe and fast transportation of packages by an Unmanned Aerial Vehicle (UAV) kind quadrotor. A mathematical model and a control strategy for a special class of underactuated mechanical systems, composed of a quadrotor transporting a cable-suspended payload, are proposed. The Euler-Lagrange formulation is used to obtain the dynamic model of the system, where the integrated dynamics of the quadrotor, cable and payload are considered. An Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) is chosen because of its inherent robustness against parametric uncertainty and unmodeled dynamics. Two cases are considered to obtain two different control laws, in the first case, the designed control law depends on the swing angle of the payload, in the second case the control law does not depend on it. The control objective is to transport the payload from point to point, with swing reduction along trajectory. Experimental results using monocular vision based navigation are shown to evaluate the proposed control law.