We theoretically and numerically study the merger phenomenon of the ion-phase vortex structure in hydrogen plasma. The results indicate that the merging of vortex structures during the nonlinear evolution of ion-acoustic waves (IAW) is mainly due to two-ion decay (TID) instability. When the daughter IAWs of the TID grow to be comparable to the fundamental mode, vortex merging will occur. Furthermore, the vortex merging can abruptly convert the significant energy of the fundamental mode into subharmonic energy, resulting in saturation for the TID of the fundamental mode. After several vortex-merging processes, the system eventually evolves into a turbulent state. In particular, the TID growth rate has been improved by considering two additional second-order coupling terms in this paper, which agree much better with the simulation results. Finally, the importance of the electron kinetic effects in the TID process is also presented by comparing hybrid-Vlasov and full-Vlasov simulations.