  Explicitly time-dependent pseudo-Hermitian (TDPH) invariants theory systems,
with a time-dependent (TD) metric, is developed for a time-dependent non
Hermitian (TDNH) quantum systems. We derive a simple relation between the
eigenstates of this pseudo-Hermitien (PH) invariant and the solutions of the
Schrodinger equation. A physical system is treated in detail: the TD Swanson
model, where an explicitly TDPH invariant is derived for this system, the
eigenvalues and eigenstates of the invariant are calculated explicitly.
