Previous research has confirmed that the newly proposed pentagonal three–four strut hybrid cable dome exhibits superior static performance compared to traditional cable domes, though its dynamic characteristics still require further study. Cable domes are wind-sensitive structures, and the results of a wind-induced vibration analysis are beneficial for the selection and construction of cable domes. In this study, a finite element model of a new open-type cable dome with a span of 120 m is established. The MATLAB 2017a programming language is employed to simulate pulsating winds, followed by a nonlinear dynamic analysis to analyze the wind-induced vibrations of the structure. The reliability of the pulsating wind model is confirmed by comparing the simulated spectrum with the target spectrum. Moreover, a wind-induced vibration time history analysis is performed to obtain the node displacement and internal force of components wind vibration coefficients, aiding in the approximation of pulsating winds with average winds in a wind-resistant design. Furthermore, a parametric analysis is carried out, ranking nodes and components based on sensitivity. The result shows that the structure exhibits the strongest wind resistance when the rise–span ratio is f/l=0.07 and the thickness–span ratio is h/l=0.08. Notably, the outer upper chord node, 2a, and the inner lower chord hoop cable, H1, are identified as the most sensitive node and component within the structure, respectively. Overall, the structure demonstrates excellent wind resistance performance, and the maximum wind vibration coefficient value remains below 3.