The superconductors with the Ginzburg-Landau (G-L) parameter (κ) ∼ 1/ √ 2 exist near a critical Bogolomonyi (B) point where they show inter-type domains between type-I and type-II superconductivity. While such physics is well understood for isotropic superconductors, the experimental investigation of the physics of anisotropic superconductors near a critical B-point remains an unattained goal mainly due to the unavailability of model material systems. Theoretically, such superconductors are expected to show type-I or type-II behaviour for definite directions of an applied magnetic field. Here, from directional point-contact Andreev reflection spectroscopy and field-angle dependent ac magnetic susceptibility measurements, we show that ZrB 12 is an anisotropic superconductor, and it exhibits field-direction dependent type-I and type-II behavior.These observations match remarkably well with the theoretical expectations for an anisotropic superconductor near a critical B-point. Therefore, our results project ZrB 12 as a model material system where the physics of inter-type anisotropic superconductivity can be explored experimentally.