In this study, we discuss the psychological acceptability of an utterance strategy used by the Driving Support Agent (DSA). Previous literature regarding DSA suggests that the adoption of a small robot as a form will increase acceptability. However, the agent’s utterance has been reported as a problem faced by the user. Therefore, in this study, we designed the agent’s utterance using politeness strategy as described by Brown and Levinson’s famous sociolinguistics and pragmatics theory and analyzed its acceptability through a participant-based experiment. In this experiment, we used positive and negative politeness strategies (PPS and NPS, respectively). In general, PPS is utilized to reflect the desire to be liked/recognized by others, whereas NPS is utilized to reflect the need for not wanting to be disturbed by others. Based on our results, PPS was rated high compared to NPS (n = 197). Therefore, many participants highly evaluated PPS. However, there was a group of participants who appreciated NPS. There were also participants who evaluated the two strategies equally. The number of participants in these three groups was observed at 4:1:1. This result contributes as an index on the utterance design of the DSA.