A column and beam connection structure for connecting a steel H-beam to a column uses an external diaphragm. The external diaphragm includes a plurality of divided diaphragm segments such that each diaphragm segment has a column plate abutting on the column. A diaphragm segment which is arranged along the steel H-beam among the plurality of divided diaphragm segments has a beam plate installed in a flange of the steel H-beam. The beam plate has an end portion in which the column plate is provided. A joining surface between the diaphragm segments is placed in a vicinity of a corner portion of the column so that only the column plate of one of the diaphragm segments abuts on each column surface of the column. A joining member fastens to fix between the diaphragm segments such that contact pressure is applied from the column plates to the surface of the column.