The Shafarevich conjecture, which was proved by Faltings and Zarhin, states the finiteness of isomorphism classes of abelian varieties of a fixed dimension over a fixed number field admitting good reduction away from a fixed finite set of finite places. In this talk, we prove the Shafarevich conjecture for irreducible symplectic varieties(, which are also known as hyper-Kähler varieties,) whose second Betti numbers are greater than 4. This talk is based on joint work with Lie Fu, Zhiyuan Li, and Haitao Zou.