We propose a method to faithfully probe and quantify the non-Gaussianity of single-mode fields in the coherent-state representations based on the averaged-cumulant technique. In comparison with the previous measure, S H Xiang et al (2018 Phys. Rev. A 97 042303), we characterize the non-Gaussianity of quantum states using the kurtosis of a Gaussian operator, rather than that of a quadrature operator. As applications, we investigate the non-Gaussianities of three different non-Gaussian states: a mixture of vacuum and Fock states, Schrödinger cat states, and photon-added coherent states. It is proven that such a kurtosis is a powerful and effective measure in appraising non-Gaussianity.