This study presents, what we believe to be, a novel approach to enhance the spectrum of extraordinary terahertz transmission utilizing surface plasmon polaritons (SPPs) mode coupling in metal-dielectric compound annular hole array metamaterial. The transmitting properties of the structure are thoroughly assessed through a combination of theoretical analysis and numerical simulation, with a particular focus on understanding the surface plasmon mode coupling. Our investigation revealed the presence of propagating surface plasmon polaritons (PSPP), localized surface plasmon resonance (LSPR) and Fabry-Perot (FP) resonances within the compound layer. We find that the coupling of PSPP and LSPR modes plays a crucial role in determining the broadband nature of the structure. Interference theory is utilized to mitigate the FP resonance, while further optimization of the transmission bands is attained by implementing the impedance matching hypothesis. By adjusting the structure parameters, the effective coupling of the SPPs modes and numerous reflections in the dielectric cavity produced a remarkably smooth and transparent character, leading to a significant enhancement of transmission spectrum and a reduction in the incident loss of terahertz wave.