We present our numerical attempts to simulate the structures of a cholesteric blue phase (BP) confined in a thin cell. Our simulations are based on a Landau-de Gennes theory describing the orientational order of the liquid crystal by a second-rank symmetric tensor. When the cell thickness is small enough, of the order of the lattice constant of the bulk BP a, various exotic defect structures that do not resemble those of bulk BPs are shown to be stable. They include a hexagonal lattice of Skyrmion excitations, and arrays of disclination lines in a double-helix form. We also show the dynamics of disclination lines in a thicker cell (∼ 2.6 a) under an applied electric field. The cell before the application of an electric field accommodates disclination lines of the form similar to that of bulk BP. The electric field alters their form in a non-trivial way depending on the field strength.