To provide a doorstop structure of a rim lock capable of reducing repulsive force generated when a door on one side hits a doorstop unit of a door on the other side when closing the double doors.

This doorstop structure of the rim lock attached to the door 11a on one side of double glass doors and being hit by the door 11b on the other side when closing the doors includes a strike unit 27 provided on an indoor face of the door 11a on one side and the doorstop unit 25 provided on an outdoor face across the door 11a on one side by the strike unit 27. The doorstop unit 25 includes a body 51 attached to an outdoor face, a block 71 fixed in the inside of the body 51, and a doorstop plate 45 made of an elastic material, abutted on the block 71, held in the body 51 through a frame body 65, having a surface hitting the door 11b on the other side and formed into a flat surface, and having a rear surface abutting on the block 71 and formed by recessed and projecting face.