  In this paper, we study holomorphic discs in K3 surfaces and defined the open
Gromov-Witten invariants. Using this new invariant, we can establish a version
of correspondence between tropical discs and holomorphic discs with non-trivial
invariants. We give an example of wall-crossing phenomenon of the invariant and
expect it satisfies Kontsevich-Soibelman wall-crossing formula.
