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The phantom dark energy remarkably boosts our prehension of the accelerating Universe. Various models are widely discussed in the phantom Universe without bulk viscosity. From the hydrodynamics' point of view, it is natural to introduce the nonperfect fluid in the study of the Universe, as an ideal fluid just an approximation to the real world after all and using the generalized equation of state (EoS) with bulk viscosity, the early inflationary universe and the accelerated expansion of the late-time universe are described by many authors. In this paper, in order to investigate how the viscosity will influence the evolution of the Universe, we study a class of phantom dark energy models with bulk viscosity by the method of dynamical analysis technique. We show that there are different cosmic late-time behaviors and the stability also brings some constraints on the models. We also plot the evolutionary trajectories of this model in the statefinder parameter-planes to see the different behaviors of the models from the statefinder viewpoint.