In this paper, a model is proposed to numerically calculate the dielectrophoretic (DEP) force acting on a straight slender body in a non-uniform electric field. The induced charges are assumed to be located along the centerline of the slender body. By enforcing the boundary conditions at the interfaces of the two dielectrics, an integral equations system is obtained with the induced charge densities as unknowns. Based on the calculated induced charge densities, expressions to calculate the DEP force and torque are obtained. The calculated induced charge density of a prolate ellipsoid under a uniform electric field is compared with the analytic solution and an excellent agreement is achieved. The smaller the slenderness (the ratio of maximum radius to length of the slender body), the smaller the error is. The DEP force that a prolate ellipsoid experiences in a general electric field is numerically calculated and compared with the results obtained by the commonly accepted effective dipole moment method. The current model is expected to possess higher accuracy than the effective dipole moment method and to demand less calculation work than the Maxwell stress tensor method.