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In this paper, we consider the well-posedness of the inhomogeneous nonlinearbiharmonic Schr\"odinger equation  with spatial inhomogeneity coefficient $K(x)$ behaves like$\left|x\right|^{-b}$ for $0<b<\min \left\{\frac{N}{2},4\right\} $. We show thelocal well-posedness in the whole $H^s$-subcritical case, with $0<s\le2$. Thedifficulties of this problem come from the singularity of $K(x)$ and the lackof differentiability of the nonlinear term. To resolve this, we derive thebilinear Strichartz's type estimates for the nonlinear biharmonic Schr\"odingerequations in Besov spaces.

Bilinear Strichartz's type estimates in Besov spaces with application to inhomogeneous nonlinear biharmonic Schr\"odinger equation