This paper proposes a discontinuous Galerkin (DG) method combined with hierarchical reconstruction to simulate the fluid model of streamer discharges. To simulate the rapid transient streamer discharge process, a method with high resolution and high order accuracy is highly desired. Combining the advantages of finite volume and finite element method, DG is such a choice. A simulation of a double-headed streamer discharge in Nitrogen was performed using 2-dimensional fluid model. The preliminary results are quantitatively agreed with those obtained by finite volume method combined with moving mesh, indicating the potential of extending the method to general streamer simulations in complex geometries.