A two-dimensional detonation in H2–O2 system is simulated by a high-resolution code based on the fifth-orderweighted essentially non-oscillatory (WENO) scheme in the spatial discretization and the 3th-order additive Runge–Kutta schemes in the time discretization, by using a detailed chemical model. The effect of a concentration gradient on cellular detonation is investigated. The results show that with the increase of the concentration gradient, the cell instability of deto-nation increases and gives rise to the oscillation of average detonation velocity. After a long time, for the case of the lower gradient the detonation can be sustained, with the multi-head mode and single-head mode alteating, while for the higher gradient it propagates with a single-head mode.