A coin selecting and counting machine for selecting and counting a number of mixed coins in accordance with the kinds thereof on the basis of differences in their diameters. The coin selecting and counting machine includes a rotary disc which is made rotatable for discharging the mixed coins by the centrifugal force thereof and a selecting and counting track formed with selecting holes for receiving the discharged mixed coins to allow the same to fall into the corresponding holes, while being unidirectionally conveyed one by one. The track is composed of a guide rail section, a curved rail section and a counting rail section. The curved rail section extends between the other two rail sections for changing the moving direction of the mixed coins to force the same into contact with its curved inner wall. Thus, the coins, which might otherwise be imprecisely located widthwise of the track, can have their circumferences further forced into contact with the inner wall of the counting rail section while being selected and counted.