Older adults are vulnerable to symptoms of depression. The degree of depression is particularly high among older adults who live alone. To address this issue, various companion robots, which are capable of psychologically communicating with users, have been proposed. However, older adults' preferences on the appearance of these robots have not been systematically investigated; this forms the focus of the present study. We interviewed 191 older adults; investigated their preferences on the design elements of robots including type, weight, and material; and analyzed the data by age, gender, and living arrangement. Our primary goal was to determine how companion robots should be designed, paying special attention to older adults who live alone. Our findings indicated that those living alone prefer a bear-like robot and negative to the heavy robot. Our results suggest that companion robots need to be designed with careful consideration of older adults' physical and psychological preferences.