A numerical simulation method for one-dimensional chemical reaction fluid mechanics equations is studied. Combining ideal gas state equation and using numerical flux of HLLC solution at boundary of each element, we present an ALE discontinuous finite element method. In high-order calculations, TVD slope limiter is used to suppress non-physical oscillation that may result from numerical solutions. Numerical results show that the algorithm maintains conservation and high precision of physical quantity. It captures clearly structural characteristics of detonation waves.