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Quadcopter unmanned aerial vehicles (UAVs) systems are receiving remarkable attention from researchers due to their daily use in numerous applications, particularly at the current time where UAVs are playing a significant role in combating the COVID-19 pandemic. This paper is concerned with the problem of UAV navigation and control in the presence of uncertainty and external disturbances. It addresses this issue by proposing an improved adaptive sliding mode control (IASMC). Improved control law generates an adaptive switching gain achieving fast adaptation and robustness against both parameter uncertainties and external disturbances. Simultaneously, the control law allows for maintaining robust trajectory tracking with chattering attenuation. The performance of the proposed IASMC controller has been evaluated using a Matlab/Simulink platform. The obtained simulation results showed that the proposed IASMC control scheme as an inner loop controller is robust when dealing with uncertainties and can effectively track the desired trajectories while significantly attenuating the well-known chattering introduced by the SMC controller.