Block-wise missing data arise more frequently nowadays in high-dimensional biomedical studies, and there is an urgent need to develop efficient dimension reduction to extract important information for prediction under block-wise missing data. Existing dimension reduction methods and feature combination are ineffective for handling block-wise missing data. We propose the factor-model imputation approach targeting block-wise missing and model imputed factor regression for dimension reduction and prediction. Specifically, we first perform screening to identify the important features, impute important features based on the factor model, and then build a factor regression model to predict the response variable based on the important features imputed. The proposed method utilizes the essential information from all observed data through the factor structure model. We show that the imputed factor regression model and its prediction are consistent under regularity conditions. Moreover, we compare the proposed method with other existing approaches through simulation studies and a real data application to the Alzheimer's Disease Neuroimaging Initiative (ADNI) data.