Abstract: The study of the internal structure of nucleons is an important frontier of current theoretical and experimental research. The high-energy scattering experiments are ideal tools for exploring the structure of nucleons. A Polarized Electron Ion Collider(EicC) is proposed based on High Intensity heavy-ion Accelerator Facility(HIAF) by Institute of Modern Physics, Chinese Academy of Sciences. EicC will provide polarized electron and proton beams with a center-of-mass energy of 15 \sim 20 GeV. The luminosity is up to 2\times10^33\ \rmcm^-2\rms^-1. Effective cooling of the ion beams is needed to achieve the luminosity goal. Due to the characteristics of large initial emittance, high energy and high intensity of ion beam, EicC adopts a two-stage beam cooling scheme. First, a conventional DC electron cooler is used to significantly reduce the ion beam emittance in the Booster ring(BRing). Secondly, a high-energy bunched cooling system based on an energy recovery linear(ERL) is used to suppress the emittance growth of ion beam during the collision in the collider ring(pRing). In this paper, taking the proton beam as an example, the effects of the electron beam size, temperature, magnetic field and lattice function on the cooling rate and cooling process in the EicC beam cooling device are simulated and investigated, and finally the beam cooling parameters that meet the luminosity requirements are obtained.