  Geometrical Singular Perturbation Theory has been successful to investigate a
broad range of biological problems with different time scales. The aim of this
paper is to apply this theory to a predator-prey model of modified Leslie-Gower
type for which we consider that prey reproduces mush faster than predators.
This naturally leads to introduce a small parameter $\epsilon$ which gives rise
to a slow-fast system. This system has a special folded singularity which has
not been analyzed in the classical work of Krupa-Szmolyan. We use the blow-up
technique to visualize the behavior near this fold point $P$. Outside of this
region the dynamics are given by classical singular perturbation theory. This
allows to quantify geometrically the attractive limit-cycle with an error of
$O(\epsilon$) and shows that it exhibits the \textit{canard} phenomenon while
crossing $P$.
