It is attractive and meaningful to apply the lattice Boltzmann method (LBM) to electrohydrodynamic (EHD) problems. As an important and fundamental problem in EHD, the behavior of freely-suspended liquid drops subjected to electrostatic fields was simulated with a 2-D LBM by means of the permittivity-density relation proposed by the authors and Peng's multiphase LBM which can obtain high liquid-to-vapor density ratio and low liquid-phase compressibility. The phenomena and laws of deformation, especially the instable behavior of the liquid drops were well simulated. And two important critical parameters, i.e. the critical permittivity ratio and the critical electric-field strength were obtained. These results agree with the corresponding theories and experiments. The simulations show the particular advantages and potential of the LBM in studying multiphase electrohydrodynamic problems.