With the development of micro-optical electromechanical systems, micro-lenses with adjustable focal length have become a research hotspot in the industry. In order to improve our understanding of the dynamic feature of variable-focus liquid micro-lens, a lattice Boltzmann-electrodynamic (LB-ED) method combining the lattice Boltzmann method and electrodynamic model was proposed to study the transient process of lens driven by electrowetting on dielectric (EWOD). The multi-component lattice Boltzmann method (LBM) was used to study the motion of the lens during a focusing action which is governed by Navier-Stokes equation, and then a new distribution function was introduced to calculate the electrical force. Firstly, the EWOD effect was numerically analyzed and compared with theoretical values and experimental results. Then the influence of voltage on the focal length was studied, and the dynamic process of zoom of the lens was analyzed. Finally, effects of the viscosity of the insulating liquid on the response time and stability of the lens were investigated. Results show that the change of contact angle agreed well with Loppmann-Young equation under low voltage and saturation occurred under high voltage, which indicated that the change of contact angle was consistent with the theoretical values and experimental results and verified the correctness of the numerical method. The relationship between applied voltage and focal length was established. When the voltage was switched, the contact angle changed abruptly but it cost the system some time to respond to the change in the force at the contact point. It was found that the system was in an oscillating state when the viscosity of the insulating liquid was small, and in an over-damped state when the viscosity was large. A suitable liquid viscosity could optimize the system performance.