In this study, an improved fluid–structure interaction (FSI) analysis method is developed for a flapping wing. A co-rotational (CR) shell element is developed for its structural analysis. Further, a relevant non-linear dynamic formulation is developed based on the CR framework. Three-dimensional preconditioned Navier–Stokes equations are employed for its fluid analysis. An implicit coupling scheme is employed to combine the structural and fluid analyses. An explicit investigation of a 3D plunging wing is conducted using this FSI analysis method. A further investigation of this plunging wing is performed in relation to its operating condition. In addition, the relation between the wing’s aerodynamic performance and plunging motion is investigated.