Wire Arc Additive Manufacturing (WAAM) is well suited for the manufacture of sizeable metallic workpieces featuring medium-to-high geometrical complexity due to its high deposition rate, low processing conditions limit, and environmental friendliness. To enhance the current capability of the WAAM process for fabricating structures with complex geometry, this paper proposes a robot-based WAAM strategy adapted specifically for fabricating free-form parts with wire structures composed of multiple struts. Contributions in this work include: (i) The study of bead modelling, which establishes optimal welding parameter selection for the process; (ii) The novel manufacturing strategy, including the adaptive slicing methodology and height control system for accurately depositing every single strut; (iii) Detailed manufacturing procedures for multi-strut branch intersections as well as the collision-free path planning to control the overall fabrication process. To verify the effectiveness of this proposed WAAM approach, two complex wire structures were fabricated successfully, indicating the feasibility of the proposed fabrication strategy.