We construct explicitly the automorphism group of the folded hypercube \(FQ_n\) of dimension \(n > 3\), as a semidirect product of \(N\) by \(M\), where \(N\) is isomorphic to the Abelian group \(\mathbb{Z}_2^{n}\), and \(M\) is isomorphic to \(\mathrm{Sym}(n+1)\), the symmetric group of degree \(n+1\). Then, we will show that the folded hypercube \(FQ_n\) is a symmetric graph.