Multi-band electromagnetically induced transparency (EIT) effects have attracted widespread attention due to their great application prospects. However, their realization is mainly based on the coupling of multiple sub-resonators that typically exceed the number of transparency peaks, resulting in complex structural designs and cumbersome preparation procedures. This paper reports a simple design of a terahertz metamaterial that can produce the triple-band EIT effect using two "big-bright" mode coupling of two sub-resonators. The design adopts the classical two-layer structure. A U-shaped split-ring resonator and a fork-shaped resonator form a periodic array on the surface of the flexible organic polymer material. Three transparency peaks around 0.59 THz, 1.07 THz, and 1.34 THz are experimentally realized, and their formation mechanisms are explored. Furthermore, the triple-band EIT metamaterial was prepared by the photolithography technology and characterized by terahertz time-domain spectroscopy. Theoretical simulation results agree well with experimental results. Sensing characteristics and slow light effects of the terahertz metamaterial are further discussed experimentally. The proposed triple-band EIT metamaterial having excellent properties, including thin size, good flexibility, simple and compact structure, and high sensing sensitivity, could provide guidance for the subsequent design and implementation of multifunctional multi-band EIT metamaterials.