  We examine a rapidly rotating Bose-Einstein condensate in an anharmonic
confinement and find that many properties such as the critical rotating
frequency and phase diagram are quite different from those in a harmonic trap.
We investigate the phase transitions by means of average-vortex-approximation.
We find that the vortex lattice consists of a vortex array with a hole in the
center of the cloud as the rotating frequency $\Omega$ increases and the vortex
becomes invisible when $\Omega$ reaches some value.
