Using time operator splitting technique and weighted essentially non-oscillatory (WENO) schemes to simulate detonation with detailed chemical reaction, a time operator splitting technique is employed to decouple hydra-dynamic transport and chemical reaction, and finite volume WENO scheme is constructed for the homogeneous Euler equations with complex equation of state. And a new entropy correction method EF4 is proposed to solve the problem of the shock instability in combination with Rose scheme. The obtained front pressure and velocity of detonation waves are in good agreement with the theoretic results, the results show that the WENO finite volume scheme can be used to simulate the transmitting process of the detonation wave perfectly.