A ternary lattice Boltzmann method based on the color-gradient model was successfully established to numerically investigate the Janus droplet formation in a Y-junction microfluidic device. We first validated the model by comparing the simulation results of contact relationship of mono-dispersed droplets with the theoretical solutions, and then studied Janus droplet formation and the breakup dynamics in Y-juncfion numerically. The results showed that the Janus droplet size obeys a scaling law during the formation. The dynamic behavior of dispersed thread, including the thread tip and minimum width of thread, revealed that the breakup of the thread is a self-thinning process. The evolution of the minimum width of dispersed thread is dominated by evolution time in a power law relationship. The deep investigation of each dispersed thread indicated that the dynamic behavior of each thread is identical before the final pinch-off in the formation process.