In order to understand the performance of the dielectric barrier discharge plasma actuator (DBD PA), analytical solutions of the electrostatic field by DBD PA were derived using the Laplace equation and the electric image method. Various electrodes shapes can be composed by the solutions. Main results are: 1) Electric field by a line electrode was composed using the solutions for the point electrodes. 2) Under a certain parameter condition, streamwise component of the electric fields seemed to be related qualitatively to the behavior of the streamwise jet velocity experimentally observed. 3) The relative permittivity of dielectric layer was supposed to have appreciable influence on the induced jet velocity suggesting that, under elevated temperatures, the jet induced by DBD PA may behave differently from that at room temperature.