In this paper, consideration is given to the initial value problem associated with the higher-dimensional fourth-order nonlinear Schrödinger equations \(\begin{aligned} i\partial _tu-\Delta ^2u =|u |^2u, \qquad (x, t)\in \mathbb {R}^d\times \mathbb {R} \end{aligned}\) with initial data \(u_0(x)\) in the modified Gevrey spaces \(H^{\sigma ,2}(\mathbb {R}^d)\) for \(d=2,3,4\) . We show that the uniform radius of spatial analyticity \(\sigma (t)\) of solution at time t does not decay faster than \(|t|^{-\frac{1}{2}}\) as \(|t| \rightarrow \infty \) . Our proof relies on approximate conservation law in modified Gevrey spaces, space-time estimates and Sobolev embedding.
