Double-bind situations, which have been considered in family therapy as a cause of negative influences into humans, can happen even in human-agent interaction, in particular, under mental therapeutic contexts. This paper reports a psychological experiment to investigate their influences into human subjects? impression evaluation of agents, while taking into account computer anxiety as one of human personal traits and face image animation as one of agent characteristics. Experimental results indicated that subjects with higher computer anxiety had more negative impression for the agent with face image animation than the one without face images. We discuss its implication on agent design, in particular, mental therapeutic agents.