The mixing characteristics of two initially stratified miscible fluids in a closed container vibrated horizontally are studied numerically by a validated computational fluid dynamics model. The flow characteristics and interfacial dynamics in the closed vibrating container are analyzed, and the effects of vibration parameters and gravity on mixing efficiency are evaluated both quantitatively and qualitatively. The results show that interfacial instability occurs in the closed container, which leads to interfacial deformation and breakup and quickens mixing. Two distinct stages of the mixing process can be observed in the closed vibrating container. During the macro-mixing, an increasingly sharp gradient of the concentration field is generated. During the micro-mixing, the mixing process is dominated by the diffusion of the concentration field and ends up with a nearly homogeneous mixture. The intensification of mixing process by vibration is most pronounced in the absence of static gravity. The gravity can suppress the interfacial instability and retard the mixing process. Over the range of conditions investigated in this paper, vibration is an efficient approach for mixing miscible liquids in a closed container.