The transport of liquid plugs in microchannels is very important for many applications such as in medical treatments in airways and in extraction of oil from porous rocks. A plug of wetting and non-wetting liquids driven by a constant pressure difference through a T-shaped microchannel is studied numerically with lattice Boltzmann (LB) method. A two-phase flow LB model based on field mediators is built. Three typical flow patterns (blocking, rupture and splitting flow) of plug flow are obtained with different driving pressures. It is found that it becomes difficult for a plug with short initial plug length to leave the microchannel; the flow pattern of plug transport varies with the contact angle, especially from wetting to nonwetting; with the increase of interfacial tension, the front interface of plug moves faster; the front and rear interfaces of the plug with small viscosity ratio move faster in the microchannel than those of the plug with large viscosity ratio. The study is helpful to provide theoretical data for the design and scale-up of liquid-liquid reactors and separators.