The density limit is one of the mechanisms of plasma disruption, and there is no very well-developed theory that can explain all the density limit disruptions. Core-located electromagnetic instability excited in high-density plasma may be one of the physical mechanisms of the density limit. In this paper, we show the electromagnetic instabilities observed in the high-density plasma of the HL-2A tokamak. These pressure gradient-driven instabilities are very easily excited in high-density plasmas and are localized in the plasma core, where their frequency is positively correlated with the ion temperature, and they often exhibit "staircase" frequency-hopping behavior with fixed frequency intervals. Simulations based on the GENE program show that the electromagnetic instabilities excited in high-density plasmas are Alfven ion temperature gradient modes (AITG). The growth rates of these electromagnetic instabilities are closely related to the pressure, ion temperature gradient, and magnetic shear, which implies that their effects on the confinement performance of high-density/high-pressure plasmas can be effectively controlled and further minimized by adjusting the relevant parameters in future burning plasmas.