A multirotor unmanned aerial vehicle (UAV) slung load system (SLS) is a nonlinear dynamics with eight degrees of freedom and four inputs that can be used for load transportation. The suspended payload can be modelled as a two degree-of-freedom pendulum attached to the UAV. This paper presents a path-following control (PFC) for an SLS. The PFC renders motions along any smooth Jordan curve in R 3 for payload position controlled-invariant. This property has practical benefits over traditional time-based trajectory tracking. Furthermore, the PFC prescribes UAV yaw and a desired payload speed profiles along the path. The PFC adopts dynamic extension and input-output state feedback linearisation. The closed-loop has a 1-dimensional zero-dynamics which is shown to be bounded. Hence, the PFC error dynamics is exponentially stable. Simulations are provided to validate the design.