Asymmetric split-ring resonators (SRRs) exhibit different resonant modes and phenomena that do not have in symmetric structure, such as Fano resonance, electromagnetic induced transparency, and plasma resonance hybridization. The asymmetric SRR was first confirmed to produce narrow linewidth resonance and has a high quality factor. Then it extends to the terahertz and near infrared bands. It has been found that the most common way to modulate the electromagnetic response characteristics is to change the asymmetry of the SRR and the coupling strength between the resonators. Here we use the finite-difference time-domain (FDTD) method to simulate the electromagnetic response characteristics of asymmetric structures. When the polarization direction along the bottom bar of the U-shaped structure, there are two similar resonance dips like those in typical SRR structure. When the incident wave is perpendicular to the bottom bar, there is only one dipole resonance. However, with the broken of the symmetry, the resonant behaviors will change. In horizontal direction, both the resonant frequency and transmittance has changed. In the vertical polarization, there are three resonant dips in transmission spectrum. Meanwhile a sharp window appears in transmission spectrum. In addition, when we turn the bottom bar of the U-shaped structure into the arc shape, we just find very slight change in frequency-shift and modulation depth in both cases, showing the impact of the short arc is nearly equivalent to the linear dipole resonance. Our obtained results indicate that we could tune the electromagnetic resonances in metamaterials and the interaction mechanism with terahertz wave.