Let \(K\) be a number field and let \(p\) be a rational prime. The Hilbert \(p\)-class field tower is defined by setting \(K_p^{(0)}=K\) and \(K_p^{(n+1)}\) to be the maximal unramified abelian \(p\)-extension of \(K_p^{(n)}\) for all \(n\geq 0\). Let \(K_p^\infty=\bigcup_{i\in\mathbb N}K_p^{i}\). In this paper the authors investigate when \(G=\mathrm{Gal}(K_2^\infty/K)\) is metacyclic. They first give a necessary and sufficient condition for \(G\) being metacyclic, under the assumption that the \(2\)-rank of the class group \(C_K\) of \(K\) is \(2\), in terms of the ranks of the class groups of the quadratic subextensions of \(K_2^{(1)}\). Finally they apply this result to determine all the real quadratic fields \(\mathbb Q(\sqrt{d})\) for which \(G\) is metacyclic and nonabelian.