This paper is concerned with the long-time behavior of solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines. Thanks to the strong coupling at the boundary, it is very difficult to obtain the uniqueness of an energy solution for problem (1)-(3) even in two dimension. To overcome this difficulty, inspired by the idea of Sell's radical approach (see [49]) to the global attractor of the three dimensional Navier-Stokes equations, we prove the closedness of the set $ W $ of all global energy solutions for problem (1)-(3) equipped with some metric such that the $ \omega $-limit set of any bounded subset in $ W $ still stay in $ W, $ which is crucial to prove the existence of a global attractor for problem (1)-(3). In addition, we prove the existence of an absorbing set in $ W $ and the uniform compactness of the semigroup $ S_t $ for problem (1)-(3), which entails the existence of a global attractor in $ W $ for problem (1)-(3).