A theoretical scheme for a new surface plasmon-polariton (SPP) fiber sensor with a fiber Bragg grating imprinted into the fiber core for SPP excitation is presented for the first time to our knowledge. In our scheme the energy in the fiber core mode can be transferred to a SPP with high efficiency by means of a properly designed short-period fiber Bragg grating (SPG). Developed for the cylindrical (fiber) geometry, our scheme without loss of generality can be applied to a planar geometry. Our simulations are based on the coupled-mode method and are performed at telecommunications wavelengths.