  For the sake of hyperk{\"a}hler SYZ conjecture, finding holomorphic
Lagrangian fibrations becomes an important issue. Toric hyperk{\"a}hler
manifolds are real dimension $4n$ non-compact hyperk{\"a}hler manifolds which
are quaternion analog of toric varieties. The $n$ dimensional residue circle
action on it admitting a hyperk{\"a}hler moment map. We use the complex part of
this moment map to construct a holomorphic Lagrangian fibration with generic
fiber diffeomorphic to $(\mathbb{C}^*)^n$, and study the singular fibers.
