Based on Hamilton's principle and Kirchhoff's assumption, this paper constructs a three-dimensional coupled kinematic analysis model of anchor cable structure, and obtains the parametric excitation instability interval of the anchor cable structure under the corresponding working conditions by solving the Hill's equation system of the three-dimensional coupled kinematic analysis model of the anchor cable structure, and analyzes the parametric resonance of the structure based on the parametric excitation instability. The results show that when the parametric excitation frequency is double or triple the intrinsic frequency of any order of the anchor cable structure, the parametric excitation resonance of the structure will be triggered, and the structure will be destabilized. The initial conditions such as displacement and velocity of the anchor cable structure do not affect the reference-excitation instability of the structure, while the water body damping can increase the stability of the anchor cable structure.