This study introduces an item response theory-zero-inflated Poisson (IRT-ZIP) model to investigate psychometric properties of multiple items and predict individuals' latent trait scores for multivariate zero-inflated count data. In the model, two link functions are used to capture two processes of the zero-inflated count data. Item parameters are included to investigate item performance from both propensity and level perspectives. The application of the model was illustrated by analyzing the substance use data from the National Longitudinal Study of Youth. A simulation study based on the empirical data analysis scenario showed that the item parameters can be recovered accurately and precisely with adequate sample sizes. Limitations and future directions are discussed. (Contains 3 figures, 5 tables and 2 notes.)