In an early report, some of us have demonstrated that graphene-sheet films prepared by electrophoretic deposition (EPD) method have great potential as high-performance field emission cathode. We report that the field emission performance from such graphene-sheet films may be enhanced. We have investigated the correlation between topographic structures and local field emission characteristics of graphene-sheet films, prepared with changing EPD deposition time. Detailed experiments show that samples prepared with longer deposition time have better field emission performance. Both scanning electron microscopy and high resolution transmission electron microscopy images show that the topographic structure of the surface layer of the samples deposited with longer time is formed with higher density of graphene sheets with shorter length and fewer graphene layers, in comparison with those with shorter deposition times. Such topographic structure is found experimentally to give large field enhancement. Computer simulation further confirms that a thinner graphene sheet will give more significant geometrical field enhancement at the corner of graphene sheet. Theoretical analysis shows that in an EPD process, longer-length graphene sheets will be deposited before shorter ones, explaining why with longer deposition time, the topographic structure of surface layer consists of shorter-length graphene sheets.