The static shape of drop under electrowetting actuation is well studied and recent electrowetting theory and experiments confirm that the local contact angle (microscopic angle) is unaffected while the apparent contact angle (macroscopic angle) is characterized by the Lippmann-Young equation. On the other hand, the evolution of the drop motion under electrowetting actuation has received less attention. In this paper, we investigate the motion of a conducting water drop on an electrowetting device (EWD) using the level set method. We derive a contact line two-phase flow model under electrowetting actuation using energy dissipation by generalizing an existing contact line model without the electric field. Our model is consistent with the static electrowetting theory as the dynamic contact angle satisfies the static Young's equation under equilibrium conditions. Our steady state results show that the apparent contact angle predicted by our model satisfies the Lippmann-Young's relation. Our numerical results based on the drop maximum deformation agree with experimental observations and static electrowetting theory. Finally, we show that for drop motion our results are not as good due to the difficulty of computing singular electric field accurately. Nonetheless, they provide useful insights and a meaningful first step towards the understanding of the drop dynamics under electrowetting actuation.