We demonstrate multispectral sharp plasmon-induced transparency response in a hybrid waveguide-plasmon system. By using the classical mechanical model of coupled damped harmonic oscillators, a clear and intuitive interpretation of the construction of the double-electromagnetically induced transparency (EIT)-like phenomenon is provided. High figure of merit up to 28.8 of the system for localized plasmon resonance refractive index sensing is obtained. Narrow polarization-independent double EIT-like spectral response is constructed, which provides an efficient tool for possible applications on slow light, enhanced nonlinear effect, nanoplasmonic functional devices, and integrated optical circuit.