We use computational approaches to explore the role of a high-refractive-index dielectric TiO2 grating with deep subwavelength thickness on InSb as a tunable coupler for THz surface plasmons. We find a series of resonances as the grating couples a normally-incident THz wave to standing surface plasmon waves on both thin and thick InSb layers. In a marked contrast with previously-explored metallic gratings, we observe the emergence of a much stronger additional resonance. The mechanism of this giant plasmonic resonance is well interpreted by the dispersion of surface plasmon excited in the airTiO2InSb trilayer system. We demonstrate that both the frequency and the intensity of the giant resonance can be tuned by varying dielectric grating parameters, providing more flexible tunability than metallic gratings. The phase and amplitude of the normally-incident THz wave are spatially modulated by the dielectric grating to optimize the surface plasmon excitation. The giant surface plasmon resonance gives rise to strong enhancement of the electric field above the grating structure, which can be useful in sensing and spectroscopy applications.