Emulsion consists of drops of one liquid dispersed into another immiscible liquid, is a novel technique for producing monodisperse droplets. The aim of this research is using the Lattice Boltzmann Method (LBM) to simulate two-phase flows in micro-channels to access the emulsification process. To this approach, The Index-Function Model proposed by He, is used to simulate drop formation in emulsification process in a co-flowing micro-channel with a complex geometry and three inlets. The simulation is performed to investigate the mechanism of drop generation due to dripping and jetting modes and the mode between them. Index function model, which is a new reliable model to evaluate two-phase flows, is applied to track the motion and deformation of the interface between the two immiscible fluids. Accuracy of our results is examined by two well-known basic analytical models including Relaxation of a rectangular drop and coalescence of two static droplets. Our results indicate good agreements with analytical data. The dimensionless numbers such as Capillary and Velocity ratio were used. The Capillary number is one of the most important dimensionless numbers in determination of fluid flow characteristics in micro-channels. The simulations reproduce dripping, widening jetting and narrowing jetting simultaneously in a coflowing microchannel in agreement with the experimental ones. This indicates that index function LBM model has a good accuracy and high stability to simulate this kind of flow.