A coaxial electrical connector includes a tubular body, first, second and third insulator members, a contact piece, and a central conductor unit. The tubular body defines a through hole, and is formed with a radial hole. The first and second insulator members are mounted in the through hole and are spaced apart from each other. The third insulator member is mounted in the radial hole. The contact piece extends into the third insulator member. The central conductor unit is supported in the through hole by the first and second insulator members, and includes a first conductor component coupled telescopically to a second conductor component. The first conductor component is movable to make or break contact with the contact piece.