We perform molecular dynamics simulations for water confined between two smooth hydrophobic walls and observe two crystalline structures with one being first reported. Both of these structures obey the ice rule. The novel ice phase is a flat hexagonal-rhombic trilayer ice, obtained under 1 GPa load at wall separation of 1.0 nm. In this structure, the water molecules in the two layers next to one of the walls (outer layers) and in the middle layer form hexagonal rings and rhombic rings, respectively. For a molecule in the outer layers, three of its four hydrogen bonds are in the same layer, and the other one hydrogen bond connects to the middle layer. For a molecule in the middle layer, only two of its four hydrogen-bonds are located in the same layer, and the other two connect to two different outer layers. Despite their different motifs, the area densities of the three layers are almost equal. The other structure is a flat hexagonal bilayer ice produced at wall separation of 0.8 nm under lateral pressure of 100 MPa, analogous to a system demonstrated by Koga et al [Phys. Rev. Lett. 79, 5262 (1997)]. Both first-order and continuous phase transitions take place in these simulations.