Tokamak is considered as the most promising experimental setup for achieving controllable nuclear fusion requirements. The parameter $\beta_{\rm{N}}$ is an important parameter for tokamak devices: high $\beta_{\rm{N}}$ benefits not only to plasma fusion but also to the enhancement of fusion reaction efficiency and the facilitation of steady-state operation. The HL-2A tokamak device has achieved stable plasma with $\beta_{\rm{N}}$ exceeding than 2.5 through neutral beam injection heating, and transiently reached $\beta_{\rm{N}}$ = 3.05, with a normalized density ( $n_{\rm{e,l}}/n_{\rm{e,G}}$ ) of about 0.6, stored energy ( $W_{\rm{E}}$ ) of around 46 kJ, and confinement improvement factor ( $H_{98}$ ) of about 1.65. In this work, the integrated simulation platform OMFIT is used to analyze the plasma at $\beta_{\rm{N}}$ = 2.83 and $\beta_{\rm{N}}$ = 3.05, and the obtained $W_ {\rm{E}}$ , $n_{\rm{e,l}}/n_{\rm{e,G}}$ , $H_{98}$ , $\beta_{\rm{N}}$ , etc. are consistent with the experimental parameters. The bootstrap current ( $f_{\rm{BS}}$ ) can reach to $45{\text{%}}$ and $46{\text{%}}$ . At both of the above moments, there are ion temperature double transport barrier (DTB) generated by the coexistence of internal transport barrier (ITB) and edge transport barrier (ETB), while high $\beta_{\rm{N}}$ is usually related to DTB. In addition, the formation of ion temperature ITB in the HL-2A device is further analyzed, which is attributed to the dominance of turbulent transport in plasma transport, the suppression of turbulent transport in the core by fast ions and ${\boldsymbol E}\times{\boldsymbol B}$ shear, and the resulting improvement in confinement, thereby ultimately leading to the formation of ion temperature ITB. The ITB of ion temperature and the ETB of H-mode synergistically contribute to the creation of high $\beta_{\rm{N}}$ plasma.