Gaseous detonation propagating in an annular cylinder was studied for hydrogen/oxygen/nitrogen mixtures numerically and experimentally. In experiments performed in an annular combustor, pressure gauges were used to measure the pressure and propagation velocity, and smoked foil measurement was performed to record the cellular structure. Meanwhile, based on the two-dimensional Euler equations with detailed finite-rate chemistry, the numerical calculations were performed by a fifth-order weighted essentially non-oscillatory (WENO) scheme and a semi-implicit Runge-Kutta method. The results show that the detonation is strengthened near the outer concave wall and weakened near the inner convex wall, so that the detonation front is continuously realigning itself to the local channel axis, to maintain the detonation steadily propagates with a planar front. In addition, the local explosion occurs on the inner wall periodically, which protects the detonation from quenches. The cellular size near the outer concave wall is smaller than that near the inner convex wall.