In this paper, we consider a class of fourth order elliptic equations of Kirchhoff type with variable exponent
\[
\begin{cases}
\Delta^{2}_{p(x)}u – M \left( \int_{\Omega} \frac{1}{p(x)} |\nabla u|^{p(x)} \, dx \right) \Delta_{p(x)}u = \lambda f(x,u), & \text{in } \Omega,\\[0.8em]
u = \Delta u = 0, & \text{on } \partial \Omega,
\end{cases}
\]
where $\Omega \subset \mathbb{R}^N$, $N \ge 3$, is a smooth bounded domain, $M(t) = a + b t^{\kappa}$, $a, \kappa > 0$, $b \ge 0$, $\lambda$ is a positive parameter, $\Delta^{2}_{p(x)}u = \Delta(|\Delta u|^{p(x)-2}\Delta u)$ is the operator of fourth order called the $p(x)$-biharmonic operator, $\Delta_{p(x)}u = \mathrm{div}(|\nabla u|^{p(x)-2}\nabla u)$ is the $p(x)$-Laplacian, $p : \overline{\Omega} \to \mathbb{R}$ is a log-Hölder continuous function and $f : \Omega \times \mathbb{R} \to \mathbb{R}$ is a continuous function satisfying some certain conditions. Using Ekeland’s variational principle combined with variational techniques, an existence result is established in an appropriate function space.