Hexagonal boron nitride (h-BN), an insulating layered material with a wide band gap, is widely utilized as the substrate and gate insulator to achieve high carrier mobility in layered channel materials, especially graphene. However little study has been conducted on the statistical analysis of the breakdown voltages and the breakdown mechanism. Generally the dielectric breakdown of SiO2, conventional three-dimensional (3D) amorphous oxides is simply explained by a percolation model. It has not been determined whether the dielectric breakdowns of 2D layered materials follow the general breakdown phenomena for 3D amorphous oxides. In this study, the anisotropic dielectric breakdown of h-BN is studied. We have found that the dielectric breakdown in c axis direction using a conductive atomic force microscope proceeded in the layer-by-layer manner [1]. The obtained dielectric field strength was ~12 MV/cm, which is comparable to the conventional SiO2. On the other hand, to estimate the dielectric field strength in a direction perpendicular to c axis, voltage is applied to a relatively thick h-BN (5-60 nm) through Cr/Au electrodes fabricated on the h-BN by EB lithography. We realized that the absorbed water on h-BN significantly affect the IV characters and the breakdown voltage. After the adsorbed water was removed by the heating in vacuum, the dielectric field strength was determined to be ~ 3 MV/cm, which is the same order as that in c axis direction. This value could be increased to be ~5 MV/cm when we consider the effect of electric field concentration around the metal electrode. This difference in dielectric filed strength for two directions is due to the highly-anisotropic nature of dielectric constant[2]. Ref. [1] Y. Hattori, et al., ACS nano 2015, 9, 916. [2] Y. Hattori, et al., in preparation.