This paper describes the dependence of the rotation frequency of an m/n = 2/1 neoclassical tearing mode (NTM) on its magnetic island width in JT-60U (m and n are the poloidal and toroidal mode numbers, respectively). Throughout the experiments, the island width is actively controlled by changing the location of the electron cyclotron current drive (ECCD), based on the fact that aligned ECCD and misaligned ECCD make the NTM islands shrink and grow, respectively. The NTM frequency was found to gradually decrease with the increasing island width. While the frequency is 5.5 kHz for zero island width, it is 3 kHz for the full island width of about 15% of the plasma minor radius. Also, the mode frequency suddenly decreases (typically by 80%) shortly after the misaligned ECCD, during which the increment in the island width is only less than 10%. A sudden increase in the mode frequency is observed shortly after the ECCD turnoff, which is nearly the reverse process of the sudden decrease, but with a hysteresis in the island width at which downward and upward frequency changes occur. The downward frequency change occurs when the frequency decreases to about half of that without the NTM.