Wave groups as natural phenomenon often accompanying sea waves have enormous destructive power. So, studies on them have aroused keen interest, especially in the ocean engineering community. Most past studies mainly focused on their statistical properties, rarely on their structural features. In this work, a dataset on typical wave groups was chosen to analyze the characteristics of wave group spectra by the gradual reduction of sampling numbers, using Fast Fourier Transform (FFT) and Maximum Entropy Method (MEM). The results indicated that the wave group spectrum obviously differed from common wave spectrum. The frequency range of wave group spectrum becomes narrow obviously and the peak value of its spectrum becomes large obviously. The whole spectral shape is similar to δ function. Also, when the many component waves the wave groups contain gradually reduce to one large component wave, the analysis results showed the features of two peak spectrum. The spectra of typical wave groups consist of two frequency components with approximately the same frequencies but different amplitudes. That is to say, the typical wave group is the superposition resultant of two train waves whose frequencies are nearly the same and amplitudes are different, just like the "BEAT" in physics-which is the resultant of two simple harmonic motions with identical motion direction, different amplitudes and periods. This study demonstrated that wave group spectrum is of the shape of δ function, which has important significance for engineering design and deserve our great attention.