Rayleigh instability of a charged droplet is well known. Although the instability condition was revealed by Lord Rayleigh, how the deformation develops after the unstable state still remains a question because of its dynamic nature. Therefore, a numerical simulation method will help to study the dynamics of the deformation of a charged droplet. In this paper we reported an interesting extension of the multi-phase lattice Boltzmann method to involve the electrostatic repulsive force working on the surface of an individual liquid droplet by means of momentum modification to simulate the Rayleigh instability. The method successfully simulates the Rayleigh instability, in which a droplet is stretched into an ellipsoidal shape when the electrostatic potential exceeds the Rayleigh's threshold, whilst a droplet with less potential than the threshold deforms back to a spherical shape as the static form.