A typical MOF material, Cu-BTC has been synthesized with microwave and conventional electric heating in various conditions to elucidate, for the first time, the quantitative acceleration in the synthesis of a MOF by microwaves. The acceleration by microwaves is mainly due to rapid nucleation rather than rapid crystal growth, even though both stages are accelerated. The acceleration in the nucleation stage by microwaves is due to the very large pre-exponential factor (about 1.4 x 10(10) times that of conventional synthesis) in the Arrhenius plot. However, the activation energy for the nucleation in the case of microwave synthesis is higher than the activation energy of conventional synthesis. The large acceleration in the nucleation, compared with that in the crystal growth, is observed once again by the syntheses in two-steps (changing heating methods from microwave into conventional heating or from conventional heating into microwave heating just after the nucleation is completed). The crystal size of Cu-BTC obtained by microwave-nucleation is generally smaller than the Cu-BTC made by conventional-nucleation, probably due to rapid nucleation and the small size of nuclei with microwave-nucleation.