A new detonation model that can simulate both high and low velocity detonations is established using the least action principle. The least action principle is valid for mechanics and thermodynamics associated with a detonation process. Therefore, the least action principle is valid in detonation science. In this model, thermodynamic equilibrium state is taken as the known final point of the detonation process. Thermodynamic potentials are analogous to mechanical ones, and the Lagrangian function in the detonation process is L = T - V Under certain assumptions, the variation calculus of the Lagrangian function gives two solutions: the first one is a constant temperature solution, and the second one is the solution of an ordinary differential equation. A special solution of the ordinary differential equation is given.