Analyzing the progression of Alzheimer's disease (AD) is challenging due to lacking sensitivity in currently available measures. AD stages are typically defined based on cognitive cut-offs, but this results in heterogeneous patient groups. More accurate modeling of the continuous progression of the disease would enable more accurate patient prognosis. To address these issues, we propose a new multivariate continuous-time disease progression (MCDP) model. The model is formulated as a nonlinear mixed-effects model that aligns patients based on their predicted disease progression along a continuous latent disease timeline. The model is evaluated using long-term follow-up data from 2152 participants in the Alzheimer's Disease Neuroimaging Initiative. The MCDP model was used to simultaneously model three cognitive scales; the Alzheimer's Disease Assessment Scale-cognitive subscale, the Mini-Mental State Examination, and the Clinical Dementia Rating scale—sum of boxes. Compared with univariate modeling and previously proposed multivariate disease progression models, the MCDP model showed superior ability to predict future patient trajectories. Finally, based on the multivariate disease timeline estimated using the MCDP model, the sensitivity of the individual items of the cognitive scales along the different stages of disease was analyzed. The analysis showed that delayed memory recall items had the highest sensitivity in the early stages of disease, whereas language and attention items were sensitive later in disease.