This paper presents a design of an asymmetric metal cross unit structure, which consists of two perpendicular coplanar gold bars deposited on a quartz substrate. The conventional metal cross structure commonly suffers from significant radiation losses in LC resonance and dipole resonance, limiting the achievement of high quality factor and high transmittance in metasurface sensors. By breaking the symmetry of the traditional metal cross structure and introducing a Fano-like resonance effect, the transmission peak sensitivity of 218 GHz/RIU and the quality factor of 78.3 are achieved. The physical mechanism of the Fano resonance effect is explored by analyzing the electric field and surface current distribution of the metasurface. Furthermore, the influence of structural parameters on the transmission spectrum of the terahertz sensor is investigated, and the sensing performance of the sensor is optimized by adjusting the structural parameters. Finally, asymmetric metal cross terahertz sensors with different resonance frequencies are designed for the detection of various types of trace amino acid solutions in subsequent applications.