Autonomous vehicles use sensors and artificial intelligence to drive themselves. Surveys indicate that people are fascinated by the idea of autonomous driving, but are hesitant to relinquish control of the vehicle. Lack of trust seems to be the core reason for these concerns. In order to address this, an intelligent agent approach was implemented, as it has been argued that human traits increase trust in interfaces. Where other approaches mainly use anthropomorphism to shape appearances, the current approach uses anthropomorphism to shape the interaction, applying Gricean maxims (i.e., guidelines for effective conversation). The contribution of this approach was tested in a simulator that employed both a graphical and a conversational user interface, which were rated on likability, perceived intelligence, trust, and anthropomorphism. Results show that the conversational interface was trusted, liked, and anthropomorphized more, and was perceived as more intelligent, than the graphical user interface. Additionally, an interface that was portrayed as more confident in making decisions scored higher on all four constructs than one that was portrayed as having low confidence. These results together indicate that equipping autonomous vehicles with interfaces that mimic human behavior may help increasing people’s trust in, and, consequently, their acceptance of them.