This work reports a CFD-DEM study on the segregation and mixing of binary mixtures of particles in a bubbling fluidized bed. A simplified mixing index was applied to determine the instantaneous mixing state in the bed, with which the effects of superficial gas velocity and initial packing state on the fluidization behavior were further discussed. For the well-mixed initial conditions, the mixing index decreases with fluidization time until a dynamic equilibrium between segregation and mixing is achieved. In contrast, the mixing index first increases and then decreases with fluidization time for completely-segregated initial conditions. However, the final equilibrium between segregation and mixing will not be affected by initial packing states for a given superficial gas velocity. Moreover, the bubbling behavior shows a marked impact on segregation and mixing, i.e., mixing is enhanced during the formation and grow-up of bubbles, while segregation is strengthened during the eruption of bubbles. This makes it possible to improve the fluidization of binary mixtures of particles based on the bubbling behaviors in the fluidized bed.