Unmanned aerial vehicles (UAVs) have been used to transport a variety of payloads, including medical materials, foods, and different electronic devices. This type of innovation generates important concerns regarding payload integrity, mainly when involving medical goods that can be affected by vibration. This paper presents the flight dynamics of suspended payload carried by an UAV, considering a flexible attachment between a quadrotor and its payload. Adaptive sliding mode control (ASMC) is proposed to enhance the trajectory tracking and consequently minimize the payload vibration. Adaptive coefficients are introduced to compensate the payload dynamics and uncertainties, which are computed for each proposed trajectory and cargo mass. The proposed adaptive control can efficiently compensate the extra dynamics and uncertainties caused by the attached payload, regardless of the chosen trajectory and weight of the cargo. A root mean square–based index is used to quantitatively evaluate the oscillations. The results show a significant attenuation of the undesired oscillations up to 27%, when the adaptive control is used. Therefore, the use of the proposed ASMC aims to guarantee an improved trajectory tracking and the attenuation of residual oscillations on the main state variables, allowing to be safely employed for transporting several types of medicines, including those sensitive to vibration and those that are dropped during a flight.