We performed an experiment of broadband dielectric relaxation spectroscopy (BDS) to study the molecular dynamics of an aqueous pullulan solution as a function of pullulan concentration. The frequency range of the BDS experiment is 40 Hz to 50 GHz, and the solution temperature is set at T = 25.0 degrees C. Two relaxation processes originating from pullulan and water molecules are obtained in the megahertz and gigahertz regions, respectively. Additionally, the electrode polarization and the contribution of dc conductivity are also observed at lower frequencies. The relaxation process at a frequency higher than 10 GHz is associated with the primary process of water (h-process), and that at 100 MHz is attributed to the local chain motion of pullulan (m-process). Impurities in the aqueous solutions, which are practically disregarded in the analysis of polysaccharide solutions, affect the quality of the relaxation spectrum. Thus, the purification of pullulan sample is carried out by methanol precipitation from aqueous pullulan solution. This iterative purification reduces the contributions of electrode polarization and DC conductivity, which enables the clear observation of the relaxation of the m-process. It was found that the relaxation times of the m- and h-processes increase with pullulan concentration. The relaxation strength of the m-process shows increasing behavior with increasing pullulan concentration, whereas the relaxation strength of the h-process decreases with increasing pullulan concentration. It is suggested that the relaxation strength of the m-process is mainly determined by the magnitude of the dipole moment of solvent molecules. The relaxation process of water (h-process) is affected by the interactions of pullulan chains. The interdependence between the h- and m-processes is discussed with respect to the findings of recent dielectric relaxation studies on aqueous polymer solutions.