This article proposes an adaptive controller for a quadrotor UAV for carrying unknown payloads while tracking any trajectory. The proposed adaptive controller is robust to modeling uncertainties and does not require any a priori knowledge of the bounds of the uncertainties. The controller is also robust to time-varying delays without any constraint on the derivative of the time delay. In addition, the stability of the closed-loop system is analyzed via a Lyapunov-like method. The controller’s performance is verified using a simulated quadrotor model in MATLAB in three different scenarios with varying time delays and parametric uncertainties.