Extraordinary optical transmission (EOT) through a metallic nano-slit or nano-slit arrays has become an efficient method to manipulate the light on a subwavelength scale. While a variety of nano-devices based on surface plasmon polaritons (SPPs) could be an ideal candidate for the next-generation ultra-compact integrated photonic circuits, this EOT phenomenon is also generally attributed to the excitation of SPPs in the nano-slit. Thus, due to its being compact in structure and amenable to integrate with other nano-devices, single nano-slit can be implemented to construct an optical source in the nano-device based on SPPs. However, the transmission through an isolated nano-slit is too low to be practically used. The main reason is that the excitation efficiency of SPPs in the nano-slit is not high enough. In fact, one of the key issues is how to enhance the excitation efficiency in a nano-slit. In this paper, a novel method and the related structure are proposed to effectively enhance the EOT in a single nano-slit by improving the excitation efficiency of SPPs. This structure is made up of a silver film on a distributed Bragg reflector (DBR), where a single nano-slit is imbedded in the silver film. Under the illumination of a TM polarized light from the DBR side of this structure, the Tamm plasmon polaritons (TPPs) at the interface between the silver film and the DBR and the SPPs in the nano-slit can be excited simultaneously. The TPP is another surface mode, which describes how an electromagnetic field is localized at the boundary of silver film and the DBR. In this structure, coupling between the TPPs and the SPPs leads to the appearance of a TPP-SPP hybrid state. When the wave-vectors between the TPP and the SPP modes are matched, due to the local field enhancement of the TPP mode, the excitation efficiency of SPPs can be improved significantly. Furthermore, utilizing the quasi Fabry-Pérot (F-P) resonance in the nano-slit, where a single nano-slit can be regarded as an F-P cavity with two open ends, a high light transmission through the single nano-slit can be achieved. In the present paper, the transmission properties of the “DBR-silver nano-slit” structure are analyzed with the finite element method and the transfer matrix method. After optimizing the structure parameters, with a thickness of the silver film of 100 nm and a width of the nano-slit of 11 nm, the light transmission through the single nano-slit in this structure can be increased by about 16 times, in comparison with the light transmission through a single nano-slit in a silver film on the TiO2 substrate (without DBR). This method of enhancing the light transmission through a single nano-slit by exciting TPPs mode and utilizing its local field enhancement property, has potential applications in the polariton lasers, the nano-scale photonic integration, the near-field imaging and sensing, and other relevant areas.