Predicting future progression of brain disorders is fundamental for effective intervention of pathological cognitive decline. Structural MRI provides a non-invasive solution to examine brain pathology and has been widely used for longitudinal analysis of brain disorders. Previous studies typically use only complete baseline MRI scans to predict future disease status due to the lack of MRI data at one or more future time points. Since temporal changes of each brain MRI are ignored, these methods would result in sub-optimal performance. To this end, we propose a longitudinal-diagnostic generative adversarial network (LDGAN) to predict multiple clinical scores at future time points using incomplete longitudinal MRI data. Specifically, LDGAN imputes MR images by learning a bi-directional mapping between MRIs of two adjacent time points and performing clinical score prediction jointly, thereby explicitly encouraging task-oriented image synthesis. The proposed LDGAN is further armed with a temporal constraint and an output constraint to model the temporal regularity of MRIs at adjacent time points and encourage the diagnostic consistency, respectively. We also design a weighted loss function to make use of those subjects without ground-truth scores at certain time points. The major advantage of the proposed LDGAN is that it can impute those missing scans in a task-oriented manner and can explicitly capture the temporal characteristics of brain changes for accurate prediction. Experimental results on both ADNI-1 and ADNI-2 datasets demonstrate that, compared with the state-of-the-art methods, LDGAN can generate more reasonable MRI scans and efficiently predict longitudinal clinical measures.