In this work, we investigate the influences of the dielectric layer on the magnetic resonance of the cut-wire pair structure (CWP). The interaction between the cut-wires is modeled through a LC circuit, based on which, the magnetic resonant frequency is calculated. Furthermore, the dependence of the resonant bandwidth on the structure parameters is also determined. By tuning the dielectric layer thickness, we obtained a noticeable broadening of the negative permeability regime of 17%, which represents the enhancement of the magnetic resonance. A good agreement between the theory, simulation, and practical experiment has been demonstrated. We believe that our results should be consequential with regard to the determination of the mechanism behind the wave-matter interaction in the GHz frequency regime.