Kondo insulators have recently aroused great interest because they are promising materials that host a topological insulator state caused by the strong electron interactions. Moreover, recent observations of the quantum oscillations in the insulating state of Kondo insulators have come as a great surprise. Here, to investigate the surface electronic state of a prototype Kondo insulator YbB12, we measured the transport properties of single crystals and microstructures. In all samples, the temperature dependence of the electrical resistivity is insulating at high temperatures and the resistivity exhibits a plateau at low temperatures. The magnitude of the plateau value decreases with reducing sample thickness, which is quantitatively consistent with the surface electronic conduction in the bulk insulating YbB12. Moreover, the magnetoresistance of the microstructures exhibits a weak-antilocalization effect at low field. These results are consistent with the presence of a topologically protected surface state, suggesting that YbB12 is a candidate material for a topological Kondo insulator. The high field resistivity measurements up to µ0H = 50 T of the microstructures provide supporting evidence that the quantum oscillations of the resistivity in YbB12 occurs in the insulating bulk.