The dynamic compressive mechanical properties of alumina porous ceramic with various average pore sizes are tested at strain rates and temperatures ranging from 0.01 s−1 to 2900 s−1 and 20 °C to 850 °C, respectively. The corresponding 3d Voronoi models are employed to simulate the meso‑characteristics of cells and failure characteristics of alumina porous ceramic in multiscale. The failure in macroscale of quasi-static compression is fragmentation, and that of dynamic compression is comminution. But in mesoscale, the failure, both of quasi-static and dynamic compression, is the fracture of cell walls. Its dynamic strength increases with the increase of strain rate, but decreases with the increase of temperature and average pore size. The increase in temperature and average pore size leads to a decrease in its strain rate sensitivity. Its Young's modulus is not sensitive to the strain rate, but increases with the decrease of average pore size, and decrease with the increase of temperature, which is presented as a temperature and average pore size dependent function. The strain rate and temperature effects are also presented by average pore size dependent functions, respectively. A constitutive model is proposed based on them. It shows that the constitutive model fits well with the experimental results.