Coaxial connector comprising a signal contact member having a connecting terminal portion and a contacting terminal portion, a grounding contact member having an annular engaging portion for engaging with an outer contact member of a mating coaxial connector and a shell portion extending from the annular engaging portion to be connected with an outer conductor of a coaxial cable, and a housing for supporting the signal contact member and the grounding contact member. The connecting terminal portion of the signal contact member is positioned at the outside of the annular engaging portion of the grounding contact member to be connected with a core conductor of the coaxial cable and the contacting terminal portion of the signal contact member is positioned at the inside of the annular engaging portion of the grounding contact member for coming into contact with a central contact member of the mating coaxial connector.