Optical Tamm plasmon (TP) can be excited at the boundary of photonic crystal and metal film. In this work, we propose a composite structure consisting of binary Au nanodisk arrays on the top of a distributed Bragg reflector (DBR) with 19.5 pair TiO<sub>2</sub>/SiO<sub>2</sub> 1D photonic crystal. The designed structure has strong confined mode at the boundary of DBR near to the binary Au nanodisk arrays, and the bandwidth of reflection spectrum is broadened obviously compared with that of the structure of Au film on the top of DBR. The conventional TP state at the boundary of nanodisks and DBR structure are modified while decreasing the size and period of binary Au nanodisk resulting from the collective lattice resonances supported by Au nanodisk. Two TP modes at 1100 nm and 1164 nm wavelength are found in reflection spectrum corresponding to different particle radii with 120 nm and 100 nm, and as the magnitude of particle radii in the two arrays approaches gradually, only one TP mode is found, which demonstrate the in-phase and anti-phase lattice resonances in different particle radii modified the confined field distribution of Tamm state at the boundary between Au nanodisk and DBR structure, generating a hybrid mode of TP and lattice resonance based on surface plasmon resonance. Coupling of TP mode and localized lattice resonance mode leads to the appearance of dual Tamm states with only one kind period DBR structure controlled by the radii of binary Au nanodisk array.