In this paper, the development of passivity-based control (PBC) algorithms to stabilize an unmanned powered parachute aerial vehicle is presented. The equations of motion of the system are presented in both Lagrangian and Hamiltonian formalisms. The proposed controllers are based on the Hamiltonian function of the system and guarantee the parachute aircraft system stabilization. In the first control law a classic PBC strategy is proposed, and in the second, an interconnection and damping assignment-passivity-based control (IDA-PBC) is chosen because of its inherent robustness against parametric uncertainty and unmodeled dynamics. The control objective is to reach a desired final position despite the initial launch conditions. Numerical simulations with variation in the parachute mass weight and in the presence of wind are carried out to validate our proposed schemes.