Single-port surgery is a new surgical method performed by inserting several surgical tools and a laparoscope through an umbilical incision. Compared with conventional laparoscopic surgery, the smaller incision in this procedure produces a lower amount of trauma, which leads to shorter hospitalization. However, with the current laparoscopic tools and surgical robots, the surgeon must overcome several difficulties, such as a limited range of motion and collisions between the surgical instruments and the laparoscope. This paper proposes a new surgical robot system for single-port surgery that uses a novel joint mechanism. The proposed joint mechanism is suitable for surgical instruments with multiple degrees of freedom (DOF). Thus, it can prevent hysteresis of the joint and achieve more accurate motion with a large force. A 6-DOF surgical instrument with this joint mechanism can avoid collisions between surgical tools or arms and approach the surgical target more easily than a conventional straight surgical tool. The external arm with 2-DOF passive joints can extend the workspace of the system during surgery. Preliminary tests and validations were performed with a prototype of the system.