First, by using of the conventional Rowell analysis, we demonstrated that the addition of nano BN particles can effectively eliminate MgO and pores in MgB2 resulting in a very high density and good connectivity of BN-doped MgB2. Then, another method—low-frequency dielectric impedance analysis—was introduced to characterize the properties of the grain boundaries of MgB2. A comparative impedance study was performed in the frequency range from 100 Hz to 100 MHz on pure and nano BN-doped MgB2. The study revealed some following interesting results: (1) a dielectric resonance around frequency of 108 in both samples was observed, which was argued to be related to an inductance-capacitance and (2) the pure sample has two dielectric relaxations originating from intergrains, while the doped sample has only one intergranular contribution. This convinces that the electric connectivity of the doped sample is really improved by the addition of nano BN particles. Our results indicate that dielectric technique may be a useful tool to characterize the grain boundary properties and grain boundary-related properties of MgB2.