Toroidicity-induced Alfven eigen (TAE) modes are observed during minority-ion cyclotron resonance heating (ICRH) in the JT-60U. The toroidal mode numbers of TAE modes are identified as 7, 8, 9, 10 and 11 from the Doppler shift in the TAE modes with scanning toroidal rotation at a plasma current of 3 MA. The toroidal mode number of TAE modes tends to increase during a giant sawtooth by ICRH with a decreasing safety factor for the central region. The TAE mode number increases with plasma current, so that nine TAE modes are observed sequentially during a giant sawtooth at a plasma current of 4 MA, where the maximum toroidal mode number is estimated to be at least 13. There are no Alfven continuum gaps for TAE modes in the safety-factor ranges of i-1/2n<q<i+1/2n, (i=1, 2, 3, ...), except for the gaps in ellipticity-induced Alfven eigen (EAE) modes, where n is the toroidal mode number of TAE modes. Therefore, control of the q profile might provide a means of avoiding TAE modes, as long as the pressure gradient of the high-energy ions is localized.