A recent study reported that confined water nanofilms may freeze continuosly or discontinuosly depending on their densities. In this study, we report results from molecular dynamics simulations of the structures and phase transition of water confined between two graphene sheets with a separation of 1.0 nm under the influence of an electric (E) field applied along the direction parallel to the sheets. We find that confined water can form three kinds of ice phases at atmospheric pressure amorphous hexagonal, or rhombic bilayer ice, depending on the E field strength (0-1.5 V/nm). As the E-field strength changes, these ice configurations can transform into each other through a first-order phase transition. These E-field-induces water phases are different from those induced by high pressure (under high density). In addition we find that all of the three ice nanofilms melt through a first-order transition. The heating and cooling processes are accompanied by a hysteresis loop between the solid and liquid phases. A phase diagram of confined water between two graphene sheets is given in the temperature-E-field plane.