A screwless curtain control assembly comprising: a bead chain base that comprises an assembly segment on one end thereof, a plurality of first radial positioning parts disposed on the assembly segment, and a plurality of first axial positioning parts arranged at the assembly segment while the first radial positioning parts and the first axial positioning parts are set alternately; a first driving member fit on the assembly segment and having a toothed bar connected to one end thereof; a second driving member that comprises a toothed part engaged with the toothed bar of the first driving member, and an assembly end affixed thereof; and a sleeve that comprises a second cavity for mounting the first driving member and the second driving member therein, a through hole located on a bottom of the second cavity of the sleeve and used for allowing the assembly end of the second driving member to pass through to be extended from the sleeve, a plurality of second radial positioning parts disposed on one end thereof with an opening of the second cavity of the sleeve and engaged with and positioned by the first radial positioning parts of the bead chain base respectively, and a plurality of second axial positioning parts that are arranged adjacent to the second radial positioning parts and engaged with and positioned by the first axial positioning parts of the bead chain base respectively. a bead chain base that comprises an assembly segment on one end thereof, a plurality of first radial positioning parts disposed on the assembly segment, and a plurality of first axial positioning parts arranged at the assembly segment while the first radial positioning parts and the first axial positioning parts are set alternately; a plurality of first radial positioning parts disposed on the assembly segment, and a plurality of first axial positioning parts arranged at the assembly segment while the first radial positioning parts and the first axial positioning parts are set alternately; a first driving member fit on the assembly segment and having a toothed bar connected to one end thereof; a second driving member that comprises a toothed part engaged with the toothed bar of the first driving member, and an assembly end affixed thereof; and a sleeve that comprises a second cavity for mounting the first driving member and the second driving member therein, a through hole located on a bottom of the second cavity of the sleeve and used for allowing the assembly end of the second driving member to pass through to be extended from the sleeve, a plurality of second radial positioning parts disposed on one end thereof with an opening of the second cavity of the sleeve and engaged with and positioned by the first radial positioning parts of the bead chain base respectively, and a plurality of second axial positioning parts that are arranged adjacent to the second radial positioning parts and engaged with and positioned by the first axial positioning parts of the bead chain base respectively. a through hole located on a bottom of the second cavity of the sleeve and used for allowing the assembly end of the second driving member to pass through to be extended from the sleeve, a plurality of second radial positioning parts disposed on one end thereof with an opening of the second cavity of the sleeve and engaged with and positioned by the first radial positioning parts of the bead chain base respectively, and a plurality of second axial positioning parts that are arranged adjacent to the second radial positioning parts and engaged with and positioned by the first axial positioning parts of the bead chain base respectively.