The loading rate dependence of the mechanical properties of metal-organic framework (MOF) crystals is key in determining their performance in many engineering applications, which, however, remains almost unexplored. Here, in situ nanoindentation experiments were conducted to investigate the impact of loading rate on mechanical properties of HKUST-1, a classic MOF. The Young's modulus and hardness of crystalline HKUST-1 are found to stay stable or decline with decreasing loading rate by creeping when the loading rate is below a particular speed, but they significantly decrease as the loading rate grows when it has higher magnitudes. Our molecular dynamics simulations indicate that the anomalous loading rate dependence of mechanical properties is attributed to the competition between the release and transfer of latent heat from the pressure-induced amorphous HKUST-1 because the increase in local temperature at large loading rates could induce the softening of HKUST-1 and the increase in the volume of transformed materials.