A new type of optical-fiber surface-plasmon-resonance (SPR) sensor based on a thin metallic film and long-period fiber gratings for measuring small changes of refractive index of analyte is presented. This sensor simply employs a long-period fiber grating with a proper period to couple a core mode $\left({\mathrm{HE}}_{11}\right)$ to the copropagating cladding mode that can excite a surface-plasmon wave (SPW). The mainly theoretical base used to analyze this new structure is the unconjugated form of coupled-mode equations. In this new SPR sensor, the variation of the refractive index of analyte is determined by monitoring the change of the transmitted core mode power, which is calculated by unconjugated two-mode coupled-mode equations at a fixed wavelength. The numerical results have demonstrated that this new and simple configuration may be used as a highly sensitive amplitude sensor. As far as the excitation of SPW, the model of numerical simulation, and the complexity of measurement equipment are concerned, this new structure is superior to the proposed sensor, consisting of a bent polished single-mode SPR optical fiber. Furthermore, the structure can be easily adapted for a SPR fiber optical probe if a mirror is deposited on the fiber tip.