Although sarcopenia is closely linked to dementia, particularly Alzheimer disease (AD), there are few studies examining the prevalence and associated factors of sarcopenia in subjects with AD. This study aimed to investigate the prevalence of sarcopenia, factors associated with sarcopenia in elderly subjects with AD, and differences in muscle functions of the upper and lower extremities and gait speed at various stages of AD. We evaluated handgrip and knee extension strength, muscle mass, and gait speed in 285 elderly outpatients with probable AD (mean age 82. 0 ± 5.3 years), including early AD (n = 82), mild AD (n = 90), and moderate AD (n = 113), and 67 elderly outpatients with normal cognition (NC) (mean age 81.1 ± 4.7 years). Sarcopenia was defined according to the consensus of the Asian Working Group for Sarcopenia. The prevalence rate of sarcopenia was significantly higher in early AD, mild AD, and moderate AD than in NC (11% in NC, 36% in early AD, 45% in mild AD, and 60% in moderate AD of the female group, and 13% in NC, 41% in early AD, 47% in mild AD, and 47% in moderate AD of the male group). Age, body mass index, and Mini-mental state examination score were associated with sarcopenia in female or male AD groups. Decreased muscle strength without loss of muscle mass of the upper and lower extremities in the female AD group and those of the lower extremity in the AD male group were found in early and mild stages. Both muscle strength and mass decreased in the moderate AD. Low gait speed was also found in the early female and male AD which progressed with advancing dementia. Subjects with AD, even the early stages of AD, showed a high prevalence rate of sarcopenia. Higher age, lower BMI, and lower MMSE score were associated with sarcopenia in the female or male AD. There were differences in muscle functions and physical performance between the stages of the female and male AD.