An equivalent circuit model of 'U'-shaped split-ring resonators (SRR), the basic structure of SRR has been proposed and studied. The proposed model, other than traditional equivalent circuit model, has taken both the influence of geometrical parameters and dielectric substrate into account and investigated them in detail. Furthermore, the calculation formula of extra mutual inductance induced by periodic cells has been derived. The performance of the 'U'-shaped SRR analyzed by the equivalent circuit model shows a good agreement with experimental measurements and numerical simulation in terahertz region. This work presents a novel method to predict the resonance frequency of complicated SPP accurately and paves an avenue for the future terahertz devices applications.