The plasmonic nanogap antenna is an efficient radiating or receiving optical device. The resonance behavior of optical antennas is commonly attributed to the excitation of a localized surface plasmon resonance (LSPR), which can be theoretically defined as the quasi-normal mode (QNM). To clarify the physical origin of the LSPR, we build up an analytical model of the LSPR by considering a multiple scattering process of propagative surface plasmon polaritons (SPPs) on the antenna arms. The model can comprehensively reproduce the complex eigenfrequency and the field distribution of QNMs of the antenna, unveiling that the LSPR arises from a Fabry–Perot resonance of SPPs. By further applying the complex pole expansion theorem of meromorphic functions, the field of the antenna under illumination by a nearby dipole emitter can be analytically expanded with QNMs, which well predicts the frequency response of the enhancement factor of radiation. The present model establishes explicit relations between the concepts of the LSPR and the propagative SPP and integrates the advantages of the Fabry–Perot and QNM formalisms of nanogap antennas.