This article presents numerical results of detonation in a two-dimensional curved channel in order to discuss its propagation behavior and the stable propagation limit. We simulated the detonation with various channel widths in two types of the ratios of inner and outer radii (R-out/R-in), which are 1.5 and 2. Two propagation modes, named as marginal and stable modes, were observed. In marginal mode, curved detonation propagates with repetition of decay, re-ignition, and propagation. Its velocity varies from underdriven to overdriven in one cycle. In a stable mode, the detonation propagates steadily while keeping a curved shock front structure and a constant detonation velocity in the circumferential direction. The idea of quasi-steady solution to the numerical results is applied for stable detonation limit. We confirmed that the detonation propagates steadily in the case that a shock radius of the detonation front is larger than the critical value of quasi-steady solution.