Summary: In this paper we prove a higher differentiability result for the solutions to a class of obstacle problems in the form \[ \min \left\{ \int_{\Omega} F ( x , D w )\, d x : w \in \mathcal{K}_\psi ( \Omega ) \right\} \] where \(\psi \in W^{1 , p ( x )}(\Omega)\) is a fixed function called obstacle and \(\mathcal{K}_\psi(\Omega) = \{w \in W_0^{1 , p ( x )}(\Omega) + u_0 : w \geq \psi \text{ a.e. in } \Omega \}\) is the class of the admissible functions, for a suitable boundary value \(u_0\). We deal with a convex integrand \(F\) which satisfies the \(p(x)\)-growth conditions \[ | \xi |^{p ( x )} \leq F(x, \xi) \leq C(1 + | \xi |^{p ( x )}), \;\;p(x) > 1. \]