  In this paper we investigate a free boundary problem for a predator-prey
model with double free boundaries in one space dimension. This system models
the expanding of an invasive or new predator species in which the free
boundaries represent expanding fronts of the predator species and are described
by Stefan-like condition. We prove a spreading-vanishing dichotomy for this
model, namely the predator species either successfully spreads to infinity as
$t\to \infty$ at both fronts and survives in the new environment, or it fails
to establish and dies out in the long run while the prey species stabilizes at
a positive equilibrium state. The long time behavior of solution and criteria
for spreading and vanishing are also obtained.
