Abstract: The investigation of the equation of state(EoS) of nuclear matter, especially at high baryon densities is one of the hot topics in the frontier of nuclear physics. The impact of the EoS at 2~5 times saturation density \rho_0 on the two-particle correlation is discussed with the ultra-relativistic quantum molecular dynamics(UrQMD) model. Focusing on the two π Hanbury-Brown-Twiss(HBT) correlations, by adopting different EoSs, the effects of potential interaction and phase transition on the HBT correlation and the spatiotemporal properties of the emission source of π are investigated. The results show that below \sim5 \rho_0, the HBT radius and parameters are sensitive to the stiffness of the EoS. By comparing with the experiment data, first-order phase transition with a significant softening of the equation of state below 4 times nuclear saturation density can be excluded using HBT data, and the available data on the HBT radii in the investigated energy region favor a relatively stiff EoS at low densities, which then turns into a soft EoS at high densities. These results highlight that the pion's HBT radius and parameters are sensitive to the stiffness of the equation of state, and can be used to constrain and understand the equation of state in the high baryon density region.