Abstract: We present a cell-centered Lagrangian scheme for numerical simulation of condensed-explosive detonation. It utilizes finite volume method to discrete detonation equations. Velocity and pressure of grid nodes are obtained with characteristics theory of hyperbolic partial differential equations. They are used to update position of grid nodes and calculate numerical flux of grid cells. Solution of grid nodes obtained by characteristics theory is a "genuinely multi-dimensional" theoretical solution, which is a generalization of one-dimensional Godunov scheme in two-dimensional Riemann problem. Semi-discrete system of detonation equations obtained by finite volume scheme is solved with an implicit-explicit Runge-Kutta method. Convection terms are explicitly treated, and stiff source terms of chemical reactions are implicitly treated. The numerical schemes select ZND model for detonation, JWL equations of state for unreacted explosives and detonation products, and use Ignition-Growth model to simulate evolution process in reaction zone. Typical numerical results show that the cell-centered Lagrangian scheme simulates condensed-explosive detonation problems well.