In this work, we consider the population-dispersal dynamics for predator- prey interactions in a two-patch  environment.  On  each  fragmented  patch,  there  is  a  two-species  predator-prey ecological  system.  It  is  assumed  that  the  predator  species  are  mobile.  The  existence  and  local dynamics of boundary equilibria and interior equilibria with respect to parameters are completely classified.  Moreover,  global  extinction  results  are  established  analytically.  In  particular,  the phenomenon of over-exploitation is also found in these discrete patches models. Finally, some biological interpretations are discussed.