Summary: Let \(q \geq 2\) be an integer, \(\chi \) be a Dirichlet character modulo \(q\), and let \(m\), \(n\) be arbitrary integers. The general Kloosterman sum \(K(m, n, \chi;q)\) is defined by \[ K(m, n, \chi;q)=\sum_{a=1}^q{}^\prime \chi (a)e\left(\frac{ma+n\bar a}{q}\right), \] where \(\sum^\prime\) denotes the summation over all \(a\) with \(\left({a, q} \right)=1\), \(e(y)=\text{e}^{2\pi{\text{i}}y}\), \({\bar a}\) is the inverse of \(a\) modulo \(q\) such that \(a\bar a \equiv 1({\bmod\; q} )\) and \(1 \leq \bar a \leq q\). In this paper we study the mean value \[ \sum_{m=1}^q \left| K(m, n, \chi;q)\right|^4, \] and give some identities.