In the present paper, noise-induced escape from the domain of attraction of a stable fixed point of a fast-slow insect outbreak system is investigated. According to Dannenberg's theory(Dannenberg PH, Neu JC, 2014), different noise amplitude ratios μ lead to the change of the Most Probable Escape Path(MPEP). Therefore, the research emphasis of this paper is to extend their study and discuss the changes of the MPEPs in more detail. Firstly, the case for μ=1, wherein the MPEP almost traces out the critical manifold, is considered. Via projecting the full system onto the critical manifold, a reduced system is obtained and the quasi-potential of the full system can be partly evaluated by that of this reduced system. In order to test the accuracy of the computed MPEP, a new relaxation method is then presented. Then, as μ converges to zero, an improved analytical method is given, through which a better approximation for the MPEP at the turning point is obtained. And then, in the case that the value of μ is moderate, wherein the MPEP will peel off the critical manifold, to determine the changing point of the MPEP on the critical manifold, an effective numerical algorithm is given. In brief, in this paper, a complete investigation on the structural changes of the MPEPs of a fast-slow insect outbreak system under different values of μ is given, and the results of the numerical simulations match well with the analytical ones.