A method of adaptive mesh is proposed and simulation of strong explosion radiation hydrodynamics based on Euler method is carried out. To demonstrate feasibility of the approach, comparisons with Zinn's numerical results are made. It shows that profiles of over-pressure and visible output power with adaptive mesh is close to those with uniform mesh with three times grid number. Meanwhile, the time consumed decrease to 1/8.5. It shows that the adaptive mesh method is feasible in high-precision numerical simulation and accuracy and efficiency are increased prominently.