This paper investigates the nonlinear vibration of an axially accelerating moving plate considering fluid–structure interaction. Nonlinear coupled equations of motion are derived by means of Kármán plate theory, the Galerkin method is then applied to transform the nonlinear partial differential equations into nonlinear ordinary differential equations. The steady-state response, various bifurcations, and chaotic behavior of the system are studied by the multiple scales method and Runge–Kutta method. The dynamical characteristics of the system are examined via response curves and bifurcation diagrams of Poincaré maps. By three-dimension bifurcation diagrams, change of motion state can be easily observed along with the variation of system parameters during the whole parametric space; meanwhile, it is found that fluctuation amplitude plays a most significant role in the change of motion state for the fluid–structure coupling system.