A surface-wave sensor based on the resonant transmission characteristics of metal hole arrays is demonstrated in the terahertz (THz) region. Since the frequency of the transmission peak of a metal hole array, which corresponds to the resonant frequency of the surface waves, is particularly sensitive to the refractive index in the vicinity of the metal surface, a very small change in the substances attached to the surface can be detected by monitoring the transmission spectrum. By attaching a layer of substance (thickness $t<5\mu \mathrm{m}$ ) much thinner than the wavelength of the THz wave ( ${\lambda }_{\mathrm{THz}}=1\mathrm{mm}$ at $0.3\mathrm{THz}$ ) to the surface of a metal hole array, we demonstrated that the existence of such a small amount of substance can be detected more easily than without the metal hole array. This demonstration of THz sensing with metal hole arrays indicates the possibility of realizing THz surface-wave sensors for biochemical molecules in the THz region.