Numerical studies were carried out to investigate the cell-like unsteady structure of oblique detonation wave (ODW) with the systematical examination of the effect of grid resolutions, To focus on the effect of activation energy, computations were carried out for a fixed flow condition of Mach number 7 flow over wedge of 30° turning angle with dimensionless heat addition of 10.0, The ODW front remains stable for low activation energy cases regardless of grid resolution, but becomes unstable for high activation energies resulting cell-like wave front structure. Similarly to ordinary normal detonation wave (NDW), intermediate activation energy results in regular oscillation, but higher one results in irregular oscillation, However, the wave structure of unstable ODW was quite different from NDW. Triple points and transverse waves propagate downstream only for the present flow conditions, and numerically simulated smoked foil record exhibits several traces of triple points those rarely intersects with each other. Several sources of the instability were conjectured from the highly refined results. Since the reaction wave behind a shock wave becomes unstable easily by any disturbances, ODW front becomes unstable and results in cell-like front structures by vorticity generated pressure waves and/or the reflected shock wave originating from the triple point. The combined effects of the different sources of instabilities exhibit highly unstable and very complex flow field behind the unstable ODW.