We investigate in detail the spectral pulsation of evolving soliton molecules in an anomalous dispersion fiber laser by utilizing the dispersive Fourier transform technique. The spectral pulsations of an evolving soliton molecule with different properties were achieved in our experiments, such as single-period and double-period pulsation. This type pulsation is characterized by the fact that the soliton molecules periodically experience oscillation in spectral profile and peak power due to the periodic vibration evolution of the internal pulses. However, the continuous weak energy exchange between the two solitons inside the soliton molecules results in an almost invariable pulse energy. In addition, analytical fitting models are given to further reveal the spectral pulsation phenomenon of the evolving soliton molecules. These experimental findings can shed some light on the dynamics of soliton molecules in fiber lasers.