Background: Higher levels of anxiety increase the risks of surgery, including morbidity and mortality. The objectives of this study were to measure anxiety and depression during the preoperative period and to identify the degree of knowledge and concerns of older patients and their family protectors regarding anesthesia, and the causes of these concerns. Methods: We administered a questionnaire to older patients scheduled to undergo surgery and their family protectors one day prior to the surgery. The questionnaire included tools for quantifying anxiety and depression (Anxiety-Visual Analogue Scale, the Amsterdam Preoperative Anxiety and Information Scale, State-Trait Anxiety Inventory Korean YZ Form, and Short Form Geriatric Depression Scale). We also asked about the concrete causes of anxiety using pre-created forms. Results: There were 140 older patients and family protectors who participated in the study. The majority of older patients (n = 114, 81.4%) undergoing surgery and their family protectors (n = 114, 81.4%) indicated that they were anxious. Most of the older patients and their family protectors responded that they had insufficient knowledge about anesthesia, and they were mostly worried about failure to awaken following surgery, and postoperative pain. Older patients with higher anxiety scores showed higher depression scores. There were significant differences in depression scores depending on the presence of cohabitating family members. Conclusions It is important to remember that older patients with higher depression scores have higher anxiety during the preoperative period.