The prediction of plastic deformation and damage evolution for metallic structural components during their service life plays a crucial role in various engineering applications. Commonly, high-temperature and cyclic mechanical loadings are applied simultaneously, demanding a fully coupled viscoplasticity-damage analysis. To this end, the work at hand proposes a viscoplasticity-damage coupled model in a thermodynamically consistent manner at finite deformations. From the theoretical aspects, the rate-dependent plasticity model is considered with nonlinear isotropic hardening and linear kinematic hardening. To address the issue of localized singularities, the Helmholtz free energy is enhanced by the nonlocal damage term based on the micromorphic extension. Using a multiplicative decomposition of the deformation gradient, both the elastic predictor and plastic corrector formulations can be described within an eigen-space. Besides, the laws of the viscoplastic flow and the local damage evolution are governed by two distinct yield surfaces, resulting in nonlinear return-mapping equations that need to be locally solved iteratively. Moreover, the proposed model is implemented into an in-house FE framework considering a fully coupled manner. Several representative examples are studied, which yield numerical robustness and good agreement with experimental data, demonstrating the capability of the present model.