Miscible fluid mixtures, like pouring honey into water, Coca Cola into strong wine, are common phenomena in our daily life. While two miscible fluids are mixed together, their appearances in terms of colors and shapes will change due to their mixing interaction. The interaction between the mixture components could be regarded as a combination of the diffusing process and demixing process. If the former dominates the interaction, it is miscible; otherwise, it is immiscible. The complex microscopic interplay between the mixture components makes the simulation highly challenging. So far, there have been some dedicated research in computer graphics dealing with immiscible mixtures, but few works have been done focusing on miscible mixtures. In this paper, for the first time, we introduce a two-fluid lattice Boltzmann method (LBM), called TFLBM, applied to miscible binary mixtures. Different from other similar methods, the viscous and diffusing properties of the fluid in our work are considered separately, so that the physical insight is exposed more clearly and rationally. In addition, the operation of LBM is mostly a linear local computation, and graphics processing unit (GPU) has been utilized to achieve real-time simulation.