The drop deformation problem in the electric field is an issue that has been widely studied and has various applications. This subject is one of the subsets of physical phenomena called Electro hydrodynamics (EHD). In the present study, the dynamic behavior of the drop is modeled numerically by considering the dynamic model of electric charges on the interface, between the drop and its outer fluid under the effect of a uniform (DC) electric field. The results given from this work are validated by both numerical and experimental results of other articles. It should be noted that both of the drop and its exterior fluid have been considered as leaky dielectric fluids and their low conductivities lead to constitution of a thin layer of the electric charges near the interface; thus, with solving the charge conservation (transfer) equation on the interface, the effect of conduction and convection of charges will be handled. In fact, surface convection of charges on the interface, dilation of the interface and traortation of electric charges due to the conduction across the interface (electromigration) will be modeled. In this work, incompressible and Newtonian fluid motion equations (Navier–Stokes) are solved in a Cartesian staggered grid by using the projection method. Moreover, the interface followed by the level set method (LSM) in an implicit way and the Ghost fluid method (GFM) is used for modeling the jump boundary condition at the interface. As a consequence, jump conditions are calculated exactly without considering any thickness for the interface by the GFM method. Also, stresses boundary conditions on the interface are the connections that link electric forces to the hydrodynamic part of problem. To ensure the accuracy of numerical method presented here, a simple problem is considered for each of the terms of the conservation equation to simulate both surface convection of charges on the interface and dilation of the interface. The results of this part show that the peroposed numerical method for solving the terms of charge conservation equation and the physical meaning of those terms supported each other. Finally, small drop deformation is investigated with changing various and effective parameters (conductivity ratio, permittivity ratio, capillary number and dimensionless electric relaxation time). It should be noted that for solving the charge traort equation, the relaxation time of electric phenomena must be equal or larger than hydrodynamic time scale. In addition, large drop deformation is studied in different ranges of capillary number. The results of the prolate deformation in this work are in good agreement with previous works; however, the oblate deformation results represent noticeable diffrences because of decreasing in the intensity of the velocity field by considering the effects of electric charges at the interface. Additionaly, for satisfying the condition of the electric relaxation time, the size of the drop is considered smaller than the same works; therefore, for the case used in this project the deformation of the drop decrease more. Keywords: Electrohydrodynamics, Electrostatics, Leaky dielectric, Traort equation, Level set method, Ghost fluid method.