This paper proposes the electromagnetically induced transparency-like (EIT-like) metamaterial with a high-quality factor (143.54), which consists of a square ring resonator (SRR) and a cross-shaped resonator (CR). The designed metamaterial generates a sharp transparency peak at 15.79 GHz. The electric field distributions reveal that appearance of the transparency window is caused by the coupling between bright mode and dark mode. Meanwhile, analysis of the surface current distributions verifies that the EIT-like effect is induced via the destructive interference of the electric dipoles . In addition, the metamaterial is equated to a circuit model, which provides a better fit to the simulated transmission spectrum. These theories fully explain the generation of the EIT-like phenomenon. Furthermore, the EIT-like metamaterial is able to detect the dielectric constant of the target analyte (glucose solution), and the sensing performance is calculated. The results demonstrate that the sensitivity (S) is 4.80 GHz/RIU and the figure of merit (FOM) reaches to 43.71. The proposed EIT-like metamaterial shows prominent sensing abilities, consequently it has potential applications in environmental monitoring, biological and chemical measurements.