In this work, we propose terahertz metamaterial sensors based on a periodic array whose unit cell consists of four split-ring resonators (SRRs) fabricated on a lossless polyimide substrate. The terahertz spectral response demonstrates that when the SRRs exhibit mirror symmetry within the unit cell, symmetry-protected bound states in the continuum (BICs) can be supported under both transverse electric (TE) and transverse magnetic (TM) polarizations. By breaking the structural symmetry through tuning the radii of the SRRs, quasi-BIC resonances are generated, providing high-Q resonances for the proposed THz metamaterial sensor. Further analysis of the surface current distributions and electromagnetic field profiles reveals the underlying physical mechanisms and pronounced near-field electromagnetic enhancement. Based on these quasi-BIC resonances, the sensing performance of the proposed metamaterial sensor is systematically evaluated, demonstrating both high quality factors and high sensitivity. The proposed sensor exhibits strong potential for applications in biological and chemical sensing in the terahertz regime.