Recently, machine-learning approaches have accelerated computational materials design and the search for advanced solid electrolytes. However, the predictors are currently limited to static structural parameters, which may not fully account for the dynamic nature of ionic transport. In this study, we meticulously curated features considering dynamic properties and developed machine-learning models to predict the ionic conductivity, σ, of solid electrolytes. We compiled 14 phonon-related descriptors from first-principles phonon calculations along with 16 descriptors related to the structure and electronic properties. Our logistic regression classifiers exhibit an accuracy of 93%, while the random forest regression model yields a root-mean-square error for log(σ) of 1.179 S/cm and R2 of 0.710. Notably, phonon-related features are essential for estimating the ionic conductivities in both models. Furthermore, we applied our prediction model to screen 264 Li-containing materials and identified 11 promising candidates as potential superionic conductors.