The diocotron instability in a low‐density non‐neutral electron plasma is examined via numerical simulations. The vortex method is used in the simulations. A special‐purpose computer, MDGRAPE‐2, accelerates the calculations of the Biot‐Savart integral in the vortex method. The diocotron modes reproduced by the simulations agree with the results obtained by the linear theory. This indicates that the simulation results are qualitatively correct. The linear growth rates of the diocotron instability in the simulations also agree with the theoretical ones. This implies that MDGRAPE‐2 gives the sufficiently accurate results for the calculations of the Biot‐Savart integral. A boundary effect from the conducting wall is discussed. It is concluded that the electric field induced by the conducting wall makes the nonlinear stage unstable and causes the clumps to merge. © 2003 American Institute of Physics