Handling missingness in multivariate categorical missing data is an important practical problem. Multiple imputation is a popular imputation method. We propose an alternative method using fractional imputation for dealing with multivariate categorical missing data, which includes model selection, parameter estimation using EM algorithm and fractional imputation. The model selection part is based on the Bayesian Information Criterion using log-linear models. We illustrate the joint modeling approach and conditional modeling approach and show that conditional modeling is computationally efficient and tractable under certain scenario in high dimensional settings. Our simulation result shows the proposed method performs better than multiple imputation using Dirichlet process model.