<p>Structural reliability assessment is of great significance for the safety and maintenance of structures. In recent years, the moment method has been rapidly developed and applied widespread for its simplicity and performance. Sometimes, the accuracy of the moment method, using only the first four moments (i.e., mean value, standard deviation, skewness, and kurtosis), is not sufficient in evaluating the reliability index of strong non-Gaussian performance functions. In this study, a method based on the quartic normal transformation (QNT) is proposed for structural reliability assessment, which enables incorporation of the first five moments, including the super-skewness, of performance function. The structural reliability index based on the QNT model is derived. The first five moments of the performance function are estimated by introducing the point estimate method. Seven engineering examples are employed to demonstrate the efficacy of the QNT. The results show that the computational efficiencies of CNT and QNT were close to each other and both superior to that of MCS. The results also show that the performance of QNT is superior to CNT in aspect of accuracy and robustness in particular to performance functions with strong non-Gaussianity.</p>