Alzheimer's disease (AD) is a progressive neurodegenerative disease characterized by cognitive decline and atrophy in the medial temporal lobe (MTL) and subsequent brain regions. Structural magnetic resonance imaging (sMRI) has been widely used in research and clinical care for diagnosis and monitoring AD progression. However, atrophy patterns are complex and vary by patient. To address this issue, researchers have made efforts to develop more concise metrics that can summarize AD-specific atrophy. Many of these methods can be difficult to interpret clinically, hampering adoption. In this study, we introduce a novel index which we call an "AD-NeuroScore," that uses a modified Euclidean-inspired distance function to calculate differences between regional brain volumes associated with cognitive decline. The index is adjusted for intracranial volume (ICV), age, sex, and scanner model. We validated AD-NeuroScore using 929 older adults from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, with a mean age of 72.7 years (SD = 6.3; 55.1-91.5) and cognitively normal (CN), mild cognitive impairment (MCI), or AD diagnoses. Our validation results showed that AD-NeuroScore was significantly associated with diagnosis and disease severity scores (measured by MMSE, CDR-SB, and ADAS-11) at baseline. Furthermore, baseline AD-NeuroScore was associated with both changes in diagnosis and disease severity scores at all time points with available data. The performance of AD-NeuroScore was equivalent or superior to adjusted hippocampal volume (AHV), a widely used metric in AD research. Further, AD-NeuroScore typically performed as well as or sometimes better when compared to other existing sMRI-based metrics. In conclusion, we have introduced a new metric, AD-NeuroScore, which shows promising results in detecting AD, benchmarking disease severity, and predicting disease progression. AD-NeuroScore differentiates itself from other metrics by being clinically practical and interpretable.