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In this paper, we consider the defocusing mass-critical nonlinearfourth-order Schr\"odinger equation. Using the $I$-method combined with theinteraction Morawetz estimate, we prove that the problem is globally well-posedin $H^\gamma(\mathbb{R}^d), 5\leq d\leq 7$ with $\gamma(d)<\gamma<2$, where$\gamma(5)=\frac{8}{5}, \gamma(6)=\frac{5}{3}$ and $\gamma(7)=\frac{13}{7}$.

Global existence for the defocusing mass-critical nonlinear fourth-order Schr\"odinger equation below the energy space