In this article, optimum adaptive sliding mode controller (ASMC) optimized by particle swarm optimization (PSO) algorithm is designed to solve the trajectory tracking control problems of a quadcopter with model parameter uncertainties. Quadcopters have nonlinear, multi-input multi-output, coupled and under-actuated dynamics. For comparison with the designed controller, an adaptive integral backstepping controller approach is applied to compensate mass and inertia uncertainties of the flying robot. These methods guarantee stability of closed-loop system and force the states to track desired reference signals. The performance of both controllers is evaluated by numerical simulations. The obtained results demonstrate the better effectiveness of the designed PSO ASMC in stabilization of tracking particularly with parameter uncertainties.