Hybrid optical-plasmonic modes have the characteristics of low loss and small mode volume, which will result in the strong localization and enhancement of electromagnetic field. Such advantages of hybrid optical-plasmonic mode are important for the enhancement of light-matter interactions. Here, terahertz (THz) hybrid modes of Fabry-Perot resonances (FPRs) and spoof surface plasmon polaritons (SSPPs) in the modified Otto scheme are investigated both in theoretical and experimental aspects. The device structure is composed of a metal grating silicon waveguide (MGSW) and a metal slit grating (MSG). The two components are vertically stacked with a variable air gap between them. The THz hybrid modes are originated from the far-field coupling of the FPRs and the SSPP supported by the air gap and the MSG, respectively. By changing the thickness of the air gap, the resonant frequency of the FPR-SSPP modes can be tuned in a frequency range of about 0.1 THz. An anti-crossing behavior between two reflection dips corresponding to the guided-mode resonance in the MGSW and the FPR-SSPP mode is observed, which leads to the narrowing of the reflection dips in the anti-crossing region. Numerical simulations show that at the resonant frequencies of FPR-SSPP mode, there is a huge volume-averaged electromagnetic energy enhancement of about 1600 times in the grooves of the MSG, which is around 8.7 times larger than that induced by the SSPP directly launched by free-space electromagnetic field. The hybrid FPR-SSPP modes can be used to construct THz sensors and detectors with high sensitivity.