The purpose of this paper is to propose a method for evaluating the appearance of an elderly companion robot based on eye tracking. Obtain the eye movement characteristics of the elderly when watching the companion robot through eye movement experiments, extract eye movement indicators, heart rate indicators and test variables, and use SPSS23.0 software platform to perform descriptive statistics and binary Logistic regression analysis on the variable information. Secondly, the appearance evaluation of the companion robot is defined as a two-category problem based on the physiological and psychological particularity of the elderly. Several factors with the strongest influence in the regression are used as the discriminant factors to establish a Fisher discriminant function model and perform experimental verification. Gender, age, education level, and heart rate indicators have no significant effect on the appearance attention of the companion robot; the total fixation duration has a significant negative effect, and the average fixation duration and the number of fixations have a significant positive effect. The accuracy of the discriminant model prediction sample compared with the actual sample is 91.0%. The Logistic-Fisher method is generally highly accurate, and it provides a feasible technical way to realize the appearance design evaluation of the elderly companion robot.