A metal-organic framework material named MIL-53(Fe), iron terephthalate, has been synthesized sovothermally at a relatively low temperature by not only conventional electric (CE) heating, but also by irradiation under ultrasound (US) and microwave (MW) conditions to gain an understanding of the accelerated syntheses induced by US and MW. The kinetics for nucleation and crystal growth were analyzed by measuring the crystallinity of MIL-53(Fe) under various conditions. The nucleation and crystal growth rates were estimated from crystallization curves of the change in crystallinity with reaction time. The activation energies and pre-exponential factors were calculated from Arrhenius plots. It was confirmed that the rate of crystallization (both nucleation and crystal growth) decreases in the order US>MW>>CE, and that the accelerated syntheses under US and MW conditions are due to increased pre-exponential factors rather than decreased activation energies. It is suggested that physical effects such as hot spots are more important than chemical effects in the accelerated syntheses induced by US and MW irradiation. The syntheses were also conducted in two steps to understand quantitatively the acceleration induced by MW and it was found that the acceleration in crystal growth is more important than the acceleration in nucleation, even though both processes are accelerated by MW irradiation.