Compared to the conventional axisymmetric dual throat nozzle, the axisymmetric divergent dual throat nozzle (ADDTN) can offer larger thrust vector angles. However, the starting problem maybe exists in the ADDTN and results in a huge thrust loss. In this paper, the ADDTN starting problem has been studied by steady and unsteady numerical simulations. The effects of nozzle geometric parameters on internal nozzle performance have been discussed in detail, including cavity divergence angle, cavity convergence angle, cavity length, expansion ratio, rounding radius at the nozzle throat, and rounding radius at the cavity bottom. And, the shock oscillation phenomenon is found inside the recessed cavity in some high-expansion ratio configurations. In addition, a bypass is proposed in this study to solve the ADDTN starting problem. The main numerical simulation results show that the expansion ratio is the most sensitive parameter affecting the starting characteristic of ADDTN, followed by the cavity divergence angle and the cavity length. And, among these parameters, the parameters of cavity convergence angle and rounding radius at the cavity bottom contribute the least to the starting problem. Besides, the ADDTN configurations of large rounding radius at the nozzle throat tend to start.