Freak waves, whose causes are not yet clearly known, represent sudden emergencies of gigantic waves on the sea surface. Previous research mainly emphasized investigation of the occurrence mechanisms of freak waves through deduction; however, this paper addresses their formation based upon an analysis of observational data gained from a data buoy. The characteristics of the wave formations for the freak waves are investigated from wavelet energy spectra. Analyses of 25 cases, derived from a data buoy off the coast of Hualien, with the maximum wave height larger than twice the significant wave height for over 2 meters. We found that freak waves exhibit characteristics of maximum wave energy and its phase spectrum concentration of the corresponding instantaneous wave energy.