Robots that can communicate with people are one of the goals reached by the technology developed for automation in work life. Experts aim to improve the communication skills of these robots further in the near future. Besides, various studies emphasize that people may interact with robots in a similar way as they interact with other people. In line of this idea, this study examines the possible causal chain in which the social anxiety affects the robot anxiety which in turn affects the attitude toward interacting with robots. Data obtained from university students were analyzed in a simple and parallel mediation model. The results showed that robot anxiety and in particular two of its sub-dimensions mediate the relationship between social anxiety and negative attitudes toward interaction with robots. Researchers should carry out new studies about the common structural characteristics of the anxiety felt by people due to interacting with humans and robots.