In recent years, a metallic single slit nanostructure or slit array structure, due to simple structure and easy-to integration, has been used to construct a light source in the nanostructures based on the surface plasmon polaritons (SPPs). However, the problem of low transmission through an isolated subwavelength single slit nanostructure is still existent. The main reason is that the excitation efficiency of SPPs in the single slit nanostructure is not too high. Therefore, how to effectively enhance the optical transmission has become a research focus. In order to further improve the transmittance of the metallic single slit nanostructure, in this paper, we improve the single slit nanostructure imbedded in the metal silver thin film on a distributed Bragg reflector (DBR) proposed in previous literature. As a result, a novel method of designing a single slit on a DBR is proposed to effectively enhance the optical transmission in a single slit by improving the excitation efficiency of SPPs. Our proposed novel structure is made up of a subwavelength single nano-slit surrounded symmetrically by a pair of grooves on both sides of metal silver film on a distributed Bragg reflector. When the TM polarized light is illuminated from the DBR side of our proposed structure to the DBR-silver slit-grooves nanostructure, the Tamm plasmon polaritons (TPPs) at the interface between the silver film and the DBR and the SPPs in the slit on the entrance side of the silver film are excited at the DBR-silver film interface, and the SPPs in the slit and grooves pair on the exit side of the silver film are excited simultaneously. In our proposed structure, coupling between the TPPs and the SPPs leads to the hybrid state of Tamm and surface plasmon polaritons in the slit and grooves. Finally, taking advantage of constructive interference between SPPs excited by the grooves and exciting hybrid states of TPPs-SPPs in the slit, due to the local field enhancement effect of the TPPs mode and the coupling effect of constructive interference between the pair grooves and the nano-slit, the excitation efficiency of the SPPs can be increased significantly. Furthermore, the quasi Fabry-Pérot resonance effect in the nano-slit is taken into consideration, and the transmittance of our proposed structure is enhanced greatly. In the present paper, the finite element method is used to study the transmission properties of the single nano-slit embedded with paired grooves on the DBR-sliver nanostructure. After a series of parameters are optimized, the maximum transmittance through the single slit in DBR-silver slit-groove nanostructure can increase to 0.22, and this transmittance is expected to be about 22 times the transmittance (0.01) of the light through a single slit in a silver film on the TiO2 substrate (without DBR and grooves), which is higher than the maximum light transsmission 0.166 given in Ref.[23]. The research results of this study have a certain application value in the fields of nano-light source design, photonic integrated circuits and optical signal transmission and so on.