Missing data and nonnormality are two common factors that can affect analysis results from structural equation modeling (SEM). The current study aims to address a challenging situation in which the two factors coexist (i.e., missing nonnormal data). Using Monte Carlo simulation, we evaluated the performance of four multiple imputation (MI) strategies with respect to parameter and standard error estimation. These strategies include MI with normality-based model (MI-NORM), predictive mean matching (MI-PMM), classification and regression trees (MI-CART), and random forest (MI-RF). We also compared these MI strategies with robust full information maximum likelihood (RFIML), a popular (non-imputation) method to deal with missing nonnormal data in SEM. The results suggest that MI-NORM had similar performance to RFIML. MI-PMM outperformed the other methods when data were not missing on the heavy tail of a skewed distribution. Although MI-CART and MI-RF do not require any distribution assumption, they did not perform well compared with the others. Based on the results, practical guidance is provided.