A novel type of ideal toroidal Alfvén eigenmode, localized in the low-shear core region of a tokamak plasma, is shown to exist, whose frequency is near the upper continuum of the toroidal Alfvén gap. This mode converts to a kinetic-type toroidal Alfvén eigenmode above a critical threshold that depends on aspect ratio, pressure gradient, and shear. Opposite to the usual ideal toroidal Alfvén eigenmode, this new mode is peaked in amplitude on the small-major-radius side of the plasma.