Simultaneous observation of Tamm plasmon (TP) and surface plasmon (SP) resonances has attracted much attention to improve the sensing performance and broaden the application field of plasmonic biosensors. Currently, enormous effort is devoted to simultaneously excite both SP and TP modes by exploiting total internal reflection. However, this method requires bulky and complicated prism or microscopy setup to fulfill the phase-matching condition, limiting the miniaturization and integration of sensors. Herein, we propose and theoretically demonstrate a nanograting-coupled plasmonic-photonic multilayer structure potentially integrated on the optical fiber tip, comprising a multilayer of photonic crystal inserted between a flat gold film and a gold nanograting. The proposed plasmonic-photonic multilayer structure enables the simultaneous excitation of TP and SP modes at the normal incidence by using zeroth and first-order diffraction light of nanograting, respectively. The resonant positions of both SP and TP modes can be independently adjusted by changing the nanograting period and the center wavelength of photonic crystal bandgap. Due to the insensitivity of TP mode to ambient surroundings, the proposed structure can be served as a self-reference SP resonance sensor for robust measurement where the sensitivity of the SP resonance sensor is determined by the wavelength shift of SP mode relative to TP mode. Moreover, the spectral overlapping of both TP and SP modes resulting in the abrupt change of reflection intensity, enables a rapid judgment to the refractive index of ambient surroundings by observing the red or blue shifts of SP resonant position relative to the case of TP. The simultaneous excitation of both TP and SP modes in the proposed structure opens a new path for improving detection accuracy and broadening application scenarios of fiber-optic SP resonance sensors.