A grating consisting of a periodic array of InSb-coated dielectric cylinders on a substrate is analyzed at THz frequencies using the frequency-dependent finite-difference time-domain method based on the trapezoidal recursive convolution technique. The transmission characteristics of an infinite periodic array are investigated not only at normal incidence but also at oblique incidence. The incident field is shown to be coupled to the substrate due to the guided-mode resonance (GMR), indicating the practical application of a grating coupler. For the sensor application, the frequency shift of the transmission dip is investigated with attention to the variation of the background refractive index. It is found that the shift of the dip involving the surface plasmon resonance is almost ten times as large as that of the dip only from the GMR. We finally analyze a finite periodic array of the cylinders. The field radiation from the array is discussed, when the field propagates through the substrate. It is shown that the radiation direction can be controlled with the frequency of the propagating field.