The invention provides a connection structure of optical fibers and a process for connecting optical fibers, by which the optical fibers are prevented from being damaged, the working time required for the connection is shortened, yield is improved, and efficiency of connection working is improved. The connection structure of optical fibers comprises 2 connecting members and brought face to face with each other and each having a through-hole and 2 optical fibers inserted into the respective through-holes of the connecting members. The 2 optical fibers are connected within the through-hole of one connecting member. The connection structure is formed by inserting optical fibers into respective through-holes of the 2 connecting members so as to locate an end surface of each optical fiber at an outlet of the through-hole or in the vicinity of the outlet, bringing the end surfaces of the 2 connecting members face to face with each other, and sliding the 2 connecting members in a direction of the center axis of the optical fibers to connect the optical fibers within the through-hole of one connecting member.