Let \(G\) be a connected, reductive algebraic group defined over \(F_ q\), \(F: G\to G\) a Frobenius morphism, and \(G^ F\) the finite group of \(F\)-fixed points. Let \(B_ 0 \supset T_ 0\) be an \(F\)-fixed Borel subgroup and maximal torus respectively, and let \(B_ 0 = T_ 0U_ 0\) where \(U_ 0\) is the unipotent radical of \(B_ 0\). A Gelfand-Graev character \(\Gamma\) of \(G^ F\) is an induced character \(\text{Ind}^{G^ F}_{U^ F_ 0}\psi\), where \(\psi\) is a non-degenerate linear character of \(U^ F_ 0\). A Gelfand-Graev character is multiplicity-free; i.e. the corresponding Hecke algebra \(H\) is commutative. The author studies the irreducible representations over \(\overline{Q}_\ell\) (where \(\ell\) is a prime not dividing \(q\)) of \(H\). He shows that every irreducible representation of \(H\) can be parametrized as \(f_{T,\theta,z} = \widehat{\theta}f_{T,z}\) where \(z\in H^ 1(F,Z(G))\), \(T\) is an \(F\)-stable maximal torus of \(G\), and \(\theta\) is an irreducible character of \(T^ F\). Next, he shows that \(f_{T,\theta,z}\) can be factorized as \(f_{T,\theta,z}=\widehat\theta f_{T,z}\) where \(f_{T,z}: H\to \overline{Q}_\ell T^ F\) is a homomorphism independent of \(\theta\), and \(\widehat{\theta}\) is the extension of \(\theta\) to a representation of \(\overline{Q}_\ell T^ F\). A formula for \(f_{T,z}(c)\), where \(c\) is a standard basis element of \(H\), is given in terms of the character \(\psi\) of \(U^ F_ 0\) corresponding to \(\Gamma\) and certain Green functions associated with \(T^ F\). The case of \(G = SL_ 2\) is worked out in detail.