It is vital to identify Mild Cognitive Impairment (MCI) subjects who will progress to Alzheimer's Disease (AD), so that early treatment can be administered. Recent studies show that using complementary information from multi-modality data may improve the model performance of the above prediction problem. However, multi-modality data is often incomplete, causing the prediction models that rely on complete data unusable. One way to deal with this issue is by first imputing the missing values, and then building a classifier based on the completed data. This two-step approach, however, may generate non-optimal classifier output, as the errors of the imputation may propagate to the classifier during training. To address this issue, we propose a unified framework that jointly performs feature selection, data denoising, missing values imputation, and classifier learning. To this end, we use a low-rank constraint to impute the missing values and denoise the data simultaneously, while using a regression model for feature selection and classification. The feature weights learned by the regression model are integrated into the low rank formulation to focus on discriminative features when denoising and imputing data, while the resulting low-rank matrix is used for classifier learning. These two components interact and correct each other iteratively using Alternating Direction Method of Multiplier (ADMM). The experimental results using incomplete multi-modality ADNI dataset shows that our proposed method outperforms other comparison methods.