An improved Eulerian method is constructed to numerically simulate the detonation course in the condensed explosives. The ignition and growth model by Lee－Tarver is used in the chemistry reaction law of explosives. The model has the following assumptions that the mixing materials are composed of the unreacted explosives and reacted products in the chemistry reaction zone, 1) have the addition of the volumes; 2) arrive at the equilibrium state about dynamics and 3) arrive at the nonequilibrium state about thermodynamics. On the basis of three assumptions, first of all, Euler equations are adopted to describe the flow motion of the mixing materials,and then the physical parameters of each material constituent, such as fraction mass, fraction volume and fraction total energy, are described through an additional set of equations. Moreover, the pressure equation about the mixing materials is coupled to the above equations, and the obtained equations of fluid flow are discretized and solved by a finite volume algorithm with high resolution and high precision. From some representative examples about unsteady detonation, the key characteristics of initiation and propagation of detonation course, such as Von Neumann spike pressure and reaction zone width can be correctly predicted by this method. The results show that the method to numerically simulate the detonation course in the condensed explosives is reasonable.