Numerical investigation was conducted on an airship of hull-fin configuration for aerodynamic and aeroelastic characteristics in three-dimensional viscous flows. The mathematical model was built and the corresponding numerical code was developed for the fluid-structure interaction problem. The governing equations of the viscous flow with LL-Low Reynolds modified model were solved by the standard SIMPLE algorithm based on the finite volume method. A fluid-structure coupled method was employed to solve the nonlinear aeroelasticity problem for the airship. The computational results of the viscous flow are in good agreement with the experimental measurements. The simulation on the aeroelastic behavior of the airship in a trimmed flight reveals the effect of structure flexibility on the aerodynamic performance.