We develop a two-patch migration model of the classical Lotka-Voltera predator-prey system with a time lag in the migration between patches. We show that when the migration rate is less than the prey growth rate the species in at least one patch survives. When the migration rate is greater than the prey growth rate, the species in both Adu A.M. Wasike et al. patches do not survive. Furthermore, when the migration rate is equal to the prey growth rate, the population will oscillate.