Several metrics of analysis of magnetic resonance imaging (MRI) have been used to assess Alzheimer's disease (AD)-related neurodegeneration. We compared four structural brain MRI analysis metrics, cortical thickness, volume, surface area, and local gyrification index (LGI), in different stages of AD-related cognitive decline. Participants with normal cognition, mild cognitive impairment, and AD were included (34 participants per group). All undertook the Consortium to Establish a Registry for Alzheimer's Disease (CERAD) battery of neuropsychological tests and brain MRI scanning. We analyzed associations between morphometric measures and CERAD total/ Mini Mental State Examination (MMSE) scores for the regions of interest (ROIs), identifying three types of curves: U-shaped, inverted U-shaped, and linear. Cortical thickness and volume analyses showed linear types in most of the significant ROIs. Significant ROIs for the cortical thickness analysis were located in the temporal and limbic lobes, whereas those for volume and surface area were distributed over more diffuse areas of the brain. LGI analysis showed few significant ROIs. CERAD total scores were more sensitive to early changes of cortical structures than MMSE scores. Cortical thickness analysis may be preferable in assessing brain structural MRI changes during AD-related cognitive decline, whereas LGI analysis may have limited capability to reflect the cognitive decrease. Our findings may provide a reference for future studies and help to establish optimal analytical approaches to brain structural MRI in neurodegenerative diseases.