Morphing wings have enjoyed much research interest due to their advantages in improving aircraft adaptability to various service environments. A single drive and continuous variable bending morphing mechanism with multiple configurations is proposed. The morphing wing designed based on this mechanism can have the advantages of lightweight, multiple configurations and smooth morphing shapes. Transient aerodynamic loads will destroy the dynamic performance of the wing during the multi-mode morphing process. Therefore, it is crucial to analyze the vibration characteristics for the reliability of the morphing wing. However, it is difficult to obtain its dynamic model and solution because of the complex configuration and the multi-mode morphing. In this paper, a mathematical model for the multi-mode morphing of the morphing mechanism based on lockable joints is described using the constraint equation firstly. Then, a rigid-flexible coupling dynamic model of the morphing wing with clearance joints is established. Finally, the influence of the infective joint and the flexible link on the vibration properties of the morphing wing is analyzed in detail. Moreover, differences in the dynamic parameters between rapid and regular actuation are discussed. The results obtained in this paper have an important engineering value for the design and manufacture of the morphing wing.