The moduli stack of Mixed Spin P-fields (MSP) provides an effective algorithm to evaluate all genus Gromov–Witten (GW) invariants of the quintic Calabi–Yau (CY) three-folds. This paper is to apply the algorithm to the genus-one case. We use the localization formula, the proposed algorithm in [ , ], and Zinger’s packaging technique to compute the genus-one GW invariants of the quintic CY three-folds. Our approach to the formula suggests a correspondence between each type of MSP graphs with each physics’ phase: CY, Landau–Ginzburg, or conifold point. In this process, new differential relations among Givental’s I-functions are also discovered.