Guidance path-planning and following are two core technologies used for controlling un-manned aerial vehicles (UAVs) in both military and civilian applications. However, only a few approaches treat both the technologies simultaneously. In this study, an innovative hybrid gradient vector fields for path-following guidance (HGVFs-PFG) algorithm is proposed to control fixed-wing UAVs to follow a generated guidance path and oriented target curves in three-dimensional space, which can be any combination of straight lines, arcs, and helixes as motion primitives. The algorithm aids the creation of vector fields (VFs) for these motion primitives as well as the design of an effective switching strategy to ensure that only one VF is activated at any time to ensure that the complex paths are followed completely. The strategies designed in earlier studies have flaws that prevent the UAV from following arcs that make its turning angle too large. The proposed switching strategy solves this problem by introducing the concept of the virtual way-points. Finally, the performance of the HGVFs-PFG algorithm is verified using a reduced-order autopilot and four representative simulation scenarios. The simulation considers the constraints of the aircraft, and its results indicate that the algorithm performs well in following both lateral and longitudinal control, particularly for curved paths. In general, the proposed technical method is practical and competitive.