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YbB₁₂ is a Kondo insulator which is theoretically predicted to host metallic surface states arising from the nontrivial band structure. Recent observation of quantum oscillations (QOs) in YbB₁₂ arouses great interest since it may indicate a Fermi surface in an insulator phase. The most important subject is to clarify whether the QOs arise from insulating bulk or metallic surface. Here we fabricated micro-devices of YbB₁₂ using focused ion beam technique and measured transport properties in high fields. All of the samples fabricated by FIB and mechanical polishing exhibit resistivity plateaus at low temperatures and residual resistivity decreases linearly as a function of thickness. These results provide evidence of 2D surface conduction in YbB₁₂. We also find the device shows positive and quasi-linear H-dependent magnetoresistance, which is attributed to the anti-weak localization of the surface electrons with spin-momentum locking. No discernible QOs are observed in this device, suggesting the QOs in single crystals arise from insulating 3D bulk.