Gromov-Witten invariants of Calabi-Yau one-folds (including elliptic curves and elliptic orbifold curves) are quasimodular forms. This can be proved using tautological relations and some ordinary differential equations in the theory of quasimodular forms, with minimal calculations. Such a method is also applicable to the Fan-Jarvis-Ruan-Witten theory of simple elliptic singularities. This allow us to prove the LG/CY correspondence for all CY one-folds using Cayley transformation of quasimodular forms, where GW/FJRW invariants are coefficients of Fourier/Taylor expansions of the same quasimodular forms. This talk is based on joint work with Jie Zhou, and Jun Li, Jie Zhou.