To provide a connector which can be managed with a comparatively small compression load at pressure contacting and which will remain in tight attachment to the connecting electrode of an IC card, even when IC card is removed and will not slip off from a connector holder.

Insulating elastomer 3 and conductive elastomer 4 are laminated alternately on the two surfaces of an insulative elastomer sheet or film 2 in such a way that their surfaces stretch parallel to one another, and thus a rod- shaped connector member is formed which is installed with its laminate surface positioned vertically so that an elastomer connector 1 for connecting an IC card is accomplished, wherein the conductive elastomer 4 is structured so that 5-20 pts.wt. carbon fibers 5 are contained, with respect to 100 pts.wt. crude material for conductive eleastomer is substantially oriented vertically relative to a connecting electrode surface 6 of the elastomer connector 1 and protrudes 10-30 μm from the connecting electrode surface of the connector 1.