This paper investigates the problem of designing a novel adaptive sliding-mode controller for heavyweight airdrop operations. The design objective is to guarantee asymptotic tracking performance of the aircraft states, in the presence of bounded nonlinear uncertainties without prior knowledge of the bounds. On the basis of feedback linearization of the aircraft–cargo model, a sliding-mode control method with projection-based adaptive function approximation is proposed. This method uses an adaptation strategy to achieve robustness against model uncertainties, and a knowledge of the bounds on the complex uncertainties is not required. Notably, the adaptation law with projection can bound the estimated function, and this avoids singularity of the control signal. Simulations are conducted under the condition that one transport aircraft performs a maximum load airdrop mission at a height of 25 m, using single-row single-platform mode. The results verify the good properties of the control method, which can meet the airdrop mission performance indexes well in the presence of ±20% aerodynamic data uncertainty and 20% actuator fault.