Connection device for connecting box to bicycle handlebar

A connection device includes a fixing board connected to a rear end of a box, a main part and a clamping unit. A locking member extends through the front board and a spring contacts against between the locking member and a rear board. Two push rods extend from a lower end of a button and slidably connected with inclined surfaces of the locking member. A safety member is connected to a mediate portion of the button and includes a spring plate which contacts against the button. The clamping unit includes two collars which are securely engaged with the adjustment plate. A bridge member is connected between the two toothed members and supported on a lower side of a handlebar stem. The clamp pieces is located at an inner side of the toothed members and mounted on a handlebar.