The analogue of electromagnetically induced transparency (EIT) is achieved in a planar terahertz resonator consisting of a square closed loop (SCL) and a split ring resonator (SRR). Finite difference time domain simulations are carried out to analyze the EIT-like effect and its potential applications as a refractive-index-based sensor. Results show that the EIT-like resonance exhibits high refractive-index sensitivity and a high figure of merit (FOM) of 4.06, higher than that for SCL (0.09) or SRR (2.48) resonators. The refractive index and dielectric loss of the substrate, which influence the sensing performance of the SCL/SRR resonator, are studied, too. A device of the SCL/SRR resonator is fabricated by using laser-induced and chemical non-electrolytic plating with copper on polyimide film. Test results conincide with simulations.