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It has been shown that carbon nanotubes exhibit good electron field emission properties, therefore, have potential applications in field emission displays and electron-beam lithography. A focusing gate is typically required to reduce the beam size for high resolution. A two-dimensional, particle-in-cell computer simulation code MAGIC was used in this work to investigate the focusing properties of the emitted electrons from a single closed-capped MWCNT in a double-gated configuration. The work function of MWCNT was taken to be 5 eV in this study. We calculated the effective beam radius at the anode plane using the electron current density as the weighting function. As a result, increasing the magnitude of the focusing voltage would cause the beam size to increase. Meanwhile, the emission current dropped monotonically from 6.85 nA to 5.8 nA as the focusing voltage varied from -60 V to -62 V. We have also varied the CNT height to investigate its effect on the beam spot size . From this study, it is clearly shown that small beam size can be obtained with an optimum focusing voltage. To achieve even smaller beam size, a much shorter MWCNT can be used or more complex multi-focusing gate designs need to be employed.