  It was known through the efforts of many works that the generating functions
in the closed Gromov-Witten theory of $K_{\mathbb P^2}$ are meromorphic
quasi-modular forms basing on the B-model predictions. In this article, we
extend the modularity phenomenon to $K_{{\mathbb P^1}\times {\mathbb P^1}},
K_{W\mathbb P[1,1,2]}, K_{\mathbb F_1}$. More importantly, we generalize it to
the generating functions in the open Gromov-Witten theory using the theory of
Jacobi forms where the open Gromov-Witten parameters are transformed into
elliptic variables.
