The phenomena of formation and detachment of droplets are one of fundamental issues in studying two-phase flows and have been seen in lots of natural phenomenon and processes, such as spraying processes, ink jet printing, emulsion, etc. Between different numerical methods, the lattice Boltzmann method (LBM) has been developed in to an alternative and promising numerical scheme for simulating multi-component fluid flows. In this project, formation and detachment of droplets were simulated, using LBM and particularly index function model. Results were validated using two-phase flows methods. After code validation, the formation and detachment of droplets in a cross-junction micro channel and under the electric field effects were studied. To survey different effects on this phenomenon, dimensionless numbers were studied. Finally, the effect of variation of permittivity, conductivity and capillary number for droplets were studied under different situations. Results show that the electric force have a positive effect in expedition of droplet formation, and also index function model proved its very use fulabilities. We have smaller drops with high frequency which shows that we can control the droplet formation.