Despite much effort and progress, the computation of higher genus Gromov-Witten invariants of quintic 3-fold remains to be a difficult problem for both mathematician and physicists. This is also true for any compact Calabi-Yau 3-fold. In this talk, I will present an approach to use quantum singularity theory built by Fan, Jarvis and myself as a tool to calculate GW-invariants of quintic 3-fold. This is a joint work with Alessandro Chiodo.