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We present and demonstrate a MEMS-based tunable terahertz metamaterial (TTM) composed of inner triadius and outer electric split-ring resonator (eSRR) structures. With the aim to explore the electromagnetic responses of TTM device, different geometrical parameters are compared and discussed to optimize the suitable TTM design, including the length, radius, and height of TTM device. The height of triadius structure could be changed by using MEMS technique to perform active tunability. TTM shows the polarization-dependent and electromagnetic induced transparency (EIT) characteristics owing to the eSRR configuration. The electromagnetic responses of TTM exhibit tunable characteristics in resonance, polarization-dependent, and electromagnetically induced transparency (EIT). By properly tailoring the length and height of the inner triadius structure and the radius of the outer eSRR structure, the corresponding resonance tuning range reaches 0.32 THz. In addition to the above optical characteristics of TTM, we further investigate its potential application in a refraction index sensor. TTM is exposed on the surrounding ambient with different refraction indexes. The corresponding key sensing performances, such as figure of merit (FOM), sensitivity (S), and quality factor (Q-factor) values, are calculated and discussed, respectively. The calculated sensitivity of TTM is 0.379 THz/RIU, while the average values of Q-factor and FOM are 66.01 and 63.83, respectively. These characteristics indicate that the presented MEMS-based TTM device could be widely used in tunable filters, perfect absorbers, high-efficient environmental sensors, and optical switches applications for THz-wave optoelectronics.