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We study the $L^1-L^\infty$ dispersive estimate of the inhomogeneousfourth-order Schr\"{o}dinger operator $H=\Delta^{2}-\Delta+V(x)$ with zeroenergy obstructions in $\mathbf{R}^{3}$. For the related propagator $e^{-itH}$,we prove that for $0<t\leq 1$, then $e^{-itH}P_{ac}(H)$ satisfies the$|t|^{-3/4}$-estimate. For $t>1$, we prove that:\,\, 1) if zero is a regularpoint of $H$, then $e^{-itH}P_{ac}(H)$ satisfies the $|t|^{-3/2}$- dispersiveestimate.\,\, 2) if zero is a resonance of $H$, there exists a time dependentoperator $F_{t}$ such that $e^{-itH}P_{ac}(H)-F_{t}$ satisfies the$|t|^{-3/2}$- dispersive estimate.\,\, 3) if zero is a resonance and~/~or aneigenvalue of $H$, then there exists a time dependent operator $G_{t}$ suchthat $e^{-itH}P_{ac}(H)-G_{t}$ satisfies the $|t|^{-3/2}$- dispersive estimate.Here $F_{t}$ and $G_{t}$ satisfy $|t|^{-1/2}$-dispersive estimates.

Dispersive estimates for inhomogeneous fourth-order Schr\"odinger operator in 3D with zero energy obstructions