We investigate a plasmonic waveguide system based on side-coupled complementary split-ring resonators (CSRR), which exhibits electromagnetically induced transparency (EIT)-like transmission. LC resonance model is utilized to explain the electromagnetic responses of CSRR, which is verified by simulation results of finite difference time domain method. The electromagnetic responses of CSRR can be flexible handled by changing the asymmetry degree of the structure and the width of the metallic baffles. Cascaded CSRRs also have been studied to obtain EIT-like transmission at visible and near-infrared region, simultaneously.