This paper presents the direct numerical simulation (DNS) of various turbulent states and structures in a rotationg plane Couette flow. The formations of turbulent patterns or roll cells in the flow were investigated at Re=750 in a range of -30 ≤Ω≤30, using a large domain size of 204.8δx2δx102.4δ. The simulations reproduced many key features in the experiment of Tsukahara, Tillmark & Alfredsson (J. Fluid Mech., vol. 648, 2010, p. 5). For stabilizing rotation with Ω=-30, a striped pattern of inter-weaved laminar-turbulent regions was observed. For stabilizing rotation with Ω=30, we found that the turbulence seems to be contained in the three-dimensional roll cells.