Metasurfaces have found extensive applications in microwave, terahertz, and optical range, serving different purposes such as filters, sensors, slow light devices, and nonlinear devices due to their distinctive electromagnetic response characteristics. Recent development requires metasurface devices to exhibit enhanced monochromaticity and stronger light interaction. Consequently, there is a growing interest in designing metasurfaces with high-quality factor ( Q-factor) resonances, considering their crucial role in achieving sharp resonances through constructing bound states in the continuum (BIC) mode. The utilization of BIC has emerged as a prominent method of designing metasurfaces with high Q-factor resonances. Due to the fact that the changes in the structural parameters of metasurfaces can simultaneously affect the resonance of two components of q-BICs, it is difficult to achieve on-demand design of operating frequency, bandwidth, and Q-factor. In this work, we investigate a novel THz metasurfaces supporting q-BIC resonance. We optimize the geometric parameters of two split ring resonators (SRRs) to tailor the operating frequencies of intrinsic resonance, and tune the coupling between different resonance modes to form the q-BIC mode resonance. The dominant modes are demonstrated by the results of multipolar decomposition calculations of the electromagnetic field distributions and scattered power at different resonant operating frequencies. In x-polarized and y-polarized incident electromagnetic wave, the normalized coupling strength ratio between the two modes are calculated by Jaynes-Cummings model to be 0.54% ( x-polarized) and 4.42% ( y-polarized) respectively, which explains the law that the resonant frequency of different modes changes with the structural parameters of SRRs device. In order to analyze the refractive index sensing capabilities of our designed metasurfaces under the incident electromagnetic waves with different polarizations, we investigate the variations of the transmitted spectrum of the metasurface with refractive index of matters. The calculated results show that the sensitivity of the metasurface is 151 GHz/RIU when the incident wave is y-polarized and 108 GHz/RIU when the incident wave is x-polarized. We realize the effective control of the operating frequency, bandwidth, and Q-factor of the q-BIC mode resonance in the transmission spectrum of the metasurface, which provides a new idea for the practical designing of terahertz metasurfaces with high Q-factor.