The optimal distribution of damping material in shell structures subject to harmonic excitations is investigated by using topology optimization method. Therein, an artificial damping material model that has a similar form as in the SIMP approach is suggested. In the optimization model, the dynamic compliance of the structure is to be minimized under a given volume constraint of the damping material and the relative densities of damping material are taken as design variables. A system reduction procedure is first performed by using the eigenmodes of the undamped system. Since the damping is non-proportional, the steady-state response and dynamic compliance of the vibrating structure are calculated by using the complex mode superposition method in the state space. The analysis of the dynamic compliance sensitivity is implemented by using the adjoint variable method. Numerical examples are presented to demonstrate the validity of the proposed method.