Summary: This paper gives an explicit formula of the \(S\)-curvature of \((\alpha,\beta)\)-metrics \(F=\alpha\varphi(\beta/\alpha)\), and proves that if \(\beta\) is a Killing 1-form of constant length with respect to \(\alpha\), then \(S=0\). Next, the author studies the \(S\)-curvature of Matsumoto-metric \(F=\alpha^2/(\alpha-\beta)\) and \((\alpha,\beta)\)-metrics \(F=\alpha+\varepsilon\beta+k(\beta^2/\alpha)\), and obtains that \(S=0\) if and only if \(\beta\) is a Killing 1-form of constant length with respect to \(\alpha\). Actually, the author also obtains the condition of the above two metrics to be weak Berwaldian. Here \(\varphi(s)\) is a \(C^\infty\) function, \(\alpha(y)=\sqrt{a_{ij}(x)y^iy^j}\) is Riemannian metric, \(\beta(y)= b_i(x)y^i\) is non zero 1-fom and \(\varepsilon,k\neq 0\) are constants.