A connection device for connecting a bag to a bicycle carriage rack includes a transverse bar connected to a back board of the bag and two hook units are connected to the transverse bar. Each hook unit includes a flexible plate and a stud extends from the flexible plate. The stud can be engaged with one of positioning holes defined in the transverse bar by pulling the flexible plate to position the hook unit to the transverse bar. The hook units hook to a side of the bicycle carriage rack. A lower part is connected to a lower portion of the back board and has a second groove with which a sliding member is slidably engaged. Each sliding member has an I-shaped member which has one end pivotably engaged therewith and the other end of the I-shaped member is engaged with a support leg of the carriage rack.