Tetrahydrofuran (THF) clathrate hydrate has been frequently used in experimental studies instead of gas hydrates because it forms at a temperature higher than the ice point under ambient pressure. In this paper, we compare the crystal growth rates of THF hydrate and ice using molecular dynamics simulations. It is demonstrated that the crystal growth of THF hydrate is much slower than that of ice. The growth rates of THF hydrate significantly deviate from a standard kinetic model known as the Wilson-Frenkel model, whereas it reproduces, the temperature dependence of the growth rate of ice. The slow crystal growth and the deviation from the Wilson-Frenkel model are attributed to the trapping of THF molecules in open small cages at the hydrate surface. We calculate the free energy profile of a THF molecule transferring from the bulk solution phase to the hydrate surface using the umbrella sampling technique. It is shown that a THF molecule trapped in an open small cage needs to cross one or two free energy barriers to escape from the surface region. We also refer to the similarity between the mechanism of slow growth of THF hydrate and the effect of kinetic hydrate inhibitors.