The pursuit of ultra-sensitive amino acid sensors is of great significance for biomedicine and chemical industry. Due to their low energy, high permeability, and fingerprint, terahertz (THz, 1 THz = 10¹² Hz) waves are excellent candidates for the nondestructive detection of biochemical substances or molecules. For metamaterials, the strong local electric field generated by surface plasmon polariton is conducive to reflect the subtle changes of the surrounding environment into the THz signal spectrum, which provides an excellent platform for the development of ultra-sensitive, nondestructive, and unlabeled amino acid sensors. Up to now, however, few researches have been reported on amino acid sensors based on THz metamaterial. Therefore, the development of ultra-sensitive sensors that can detect amino acid solutions with low concentrations is an important subject in the realm of THz functional devices. Taking full advantage of the sensitive response of the Fermi level (E_F) around the Dirac point in the graphene energy band to the sample in conjugation with the electric field strongly confined on the surface of the metamaterial, a terahertz sensor composed of graphene and metal metamaterial is proposed to realize the multi-dimensional ultra-sensitive sensing for glutamic acid. The designed sensor (denoted Dev.1) consists of a SiO₂ substrate, polyimide (PI), metal arrays, and single-layer graphene. The detailed structure parameters of each metal pattern are as follows: L₁=180 μm, L₂=150 μm, a=20 μm, b=5 μm, c=14 μm, d=5 μm, e=18.5 μm, f=30 μm (Fig.1). The thickness of the unit cell, PI, and the substrate are 0.2 μm, 8 μm, and 300 μm, respectively. THz transmission spectra of the sensors are measured by THz-time domain spectrometer, and glutamic acid solutions with seven different concentrations are prepared: C₀=0 fg/mL, C₁=1.25 $ \times $10^-1 fg/mL, C₂=2.50 $ \times $10^-1 fg/mL, C₃=1.08 $ \times $10¹ fg/mL, C₄=4.32 $ \times $10² fg/mL, C₅=3.63 $ \times $10⁵ fg/mL, C₆=1.03 $ \times $10¹² fg/mL. The simulation part is implemented by the time domain solver. For Dev.1, there is a significant resonant peak at f = 0.58 THz in the transmission spectra, which is attributed to the coupling between two groups of electrical dipole resonance modes (Fig.2(b)-(c), Fig.3). More importantly, the peak amplitude first increases and then decreases with the rising solution concentration. It means that taking $ {\Delta }{T} $ ( $ {\Delta }{T}{=}{{T}}_{{{C}}_{{i}}}{-}{{T}}_{{{C}}_{{0}}} $, where $ {{T}}_{{{C}}_{{i}}} $( $ {{T}}_{{{C}}_{{0}}} $) is transmittance for the sensor covered by C_i(C₀) glutamic acid solution) as the sensing indicator, the proposed sensor can detect the minimum value in the order of 10^-1 fg/mL. Such ultrasensitivity can be rationalized by the ultra-sensitive response of E_F around Dirac point to the surrounding environment (Fig.4) in conjugation with the confined field induced by electrical dipole induced. In addition, one can find that the slope extracted from ΔP(f) ( $ {Δ}{P}{(}{f}{)=}{{P}}_{{{C}}_{{i}}}{(}{f}{)-}{{P}}_{{{C}}_{{0}}}{(}{f}{)} $, where $ {{P}}_{{{C}}_{{i}}}{(}{f}{)} $ ( $ {{P}}_{{{C}}_{{0}}}{(}{f}{)} $) is the phase of transmitted THz for the sensor covered by C_i(C₀) glutamic acid solution vs frequency also exhibits quasi-linear dependence on C_i, and holds monotonically increasing within the range C₀-C₅(Fig.5). It demonstrates that the slope related to phase difference can be cross-verified with ∆T to realize multi-dimensional and ultra-sensitive detection of glutamic acid solution with the concentration of C₀-C₅. A multi-dimensional ultra-sensitive THz sensor composed of graphene and metal metamaterials is proposed for the detection of glutamic acid concentration. The experimental results show that there is a transmission peak at 0.58 THz in the THz transmission spectra, which originates from the coupling between two modes of electrical dipoles. With the increase of glutamic acid concentration, the transmission peak amplitude increases first and then decreases. Taking the peak amplitude as the sensing indicator, the limit of detection for the sensor can be as low as the order of 10^-1 fg/mL. The strong confined electric field on the surface of the metamaterial together with the sensitive response of the E_F in the graphene energy band to different solution concentrations causes significant changes in the electromagnetic properties of the device and the corresponding transmitted THz wave, which is the main reason for the ultra-sensitive sensing characteristics for the composite device. In addition, the effect of glutamic acid solution concentration on the phase of transmitted THz wave was also studied. The results show that the slope extracted from phase difference-frequency curves has a quasi-linear relationship with the concentration from C₀ to C₅. Therefore, it can also be utilized as an indicator to detect the concentration of the glutamic acid solution with 10^-1 fg/mL. This work has contributed to the development of THz metamaterials in amino acid sensors.