  In this paper, a data-driven method to precisely simulate the detector
response of the anti-neutron depositing in the Electromagnetic Calorimeter
(EMC)at BESIII is introduced. A large anti-neutron data sample can be selected
using the decay $J/\psi\to p\bar{n}\pi^{-}$ from the BESIII data sample of 10
billion $J/\psi$ events. The detection efficiency for and various observables
of anti-neutrons interacting in the EMC detector are simulated, taking the
correlations among the variables into consideration. The systematic uncertainty
of this data-driven simulation method is determined to be less than 1\% on
average. This method can be widely applied in physics processes that require
precise simulation of the detector response of anti-neutrons in the EMC.
