Circular cross-section plasma is the most basic form of tokamak plasma and the fundamental configuration for magnetic confinement fusion experiments. This article is based on the HL-2A limiter discharge experiments to study the magnetohydrodynamic (MHD) equilibrium and MHD instability of tokamak plasmas in circular cross-section. The results showed that when q₀=0.95, the internal kink mode of m/n=1/1 is always unstable. The increase in plasma β (=the ratio of thermal pressure to magnetic pressure) can lead to the appearance of external kink modes. The combination of axial safety factor q₀ and edge safety factor q_a determines the equilibrium configuration of the plasma and also affects the MHD stability of the equilibrium, but its growth rate is also related to the size of β. Under the condition of q_a>2 and q₀ slightly greater than 1, it is easy to achieve the stabilization of internal and surface kink modes. However the plasma becomes unstable again and the instability intensity increases as q₀ continues to increase when q₀ exceeds 1. As the poloidal specific pressure (β_p) increases, the MHD instability develops, the equilibrium configuration of MHD elongates laterally, and the Shafranov displacement increases, which in turn has the effect for suppressing instability. Calculations have shown that the maximum β value imposed by the ideal MHD mode in a plasma with free boundary in tokamak experiments is proportional to the normalized current I_N (=I_p(MA)/a (m)B₀(T)), and the maximum specific pressure is calibrated as β(max)~2.01I_N. The operational β limit of HL-2A circular cross-section plasma is approximately β_N^c≈2.0. A too high q₀ is not conducive to MHD stability and leads to a decrease in the β limit. When q₀=1.3, we obtain a maximum β_N of approximately 1.8. Finally, based on the existing circular cross-section plasma, some key factors affecting the operational β and the relationship between achievable high β and the calculated ideal β limits were discussed.