Installation structure of a glass fixing gasket and a window glass panel fixing bracket being provided in order to fix the window glass panel of a fixed window constituting the sliding window system including a segment type window frame to the window frame, as being installed between the window frame portion (1110, 1310, 1500, 1120, 1220) that supports three sides, preferably an upper side, a lower side and an outer one side, of the fixed window and a window glass panel provided as pair glass, the installation structure comprising: an outer segment insulation support inserted into the window frame of an outer portion and a central portion of the window glass, and an inner segment insulation support inserted into the window frame (1110, 1500) of an inner portion of the window glass; an insulating glass pedestal (1330; 1330-u 1330-d, 1330-s) made of an expanded plastic-based material that is inserted and installed in a space between the outer segment insulating support and the inner segment insulating support; an outer glass fixing gasket made of an expanded rubber material which is fitted to a first fitting groove formed on an outer portion of the insulating glass pedestal; a window glass panel fixing bracket made of an expanded plastic-based material having a fitting protrusion which is fitted to a second fitting groove formed on an inner portion of the insulating glass pedestal, wherein the window glass panel fixing bracket is installed in a wedge method to respond to the static pressure of the wind pressure by supporting the inner side of the window glass panel; and an inner glass fixing gasket made of an expanded rubber material coupled to a fitting groove formed in the window glass panel fixing bracket; and wherein a shape of the inner portion of the insulating glass pedestal has a reduced cross-section so as not to interfere with the central support surface (1320b-2) ^of the inner segment insulation support, when a rotational fitting end (1320b-1) of the inner segment insulating support to be subsequently coupled is rotated by a set angle and fitted to an inner locking protrusion of the window frame of the outer portion and the central portion of the window glass. an outer segment insulation support inserted into the window frame of an outer portion and a central portion of the window glass, and an inner segment insulation support inserted into the window frame (1110, 1500) of an inner portion of the window glass; an insulating glass pedestal (1330; 1330-u 1330-d, 1330-s) made of an expanded plastic-based material that is inserted and installed in a space between the outer segment insulating support and the inner segment insulating support; an outer glass fixing gasket made of an expanded rubber material which is fitted to a first fitting groove formed on an outer portion of the insulating glass pedestal; a window glass panel fixing bracket made of an expanded plastic-based material having a fitting protrusion which is fitted to a second fitting groove formed on an inner portion of the insulating glass pedestal, wherein the window glass panel fixing bracket is installed in a wedge method to respond to the static pressure of the wind pressure by supporting the inner side of the window glass panel; and an inner glass fixing gasket made of an expanded rubber material coupled to a fitting groove formed in the window glass panel fixing bracket; and wherein a shape of the inner portion of the insulating glass pedestal has a reduced cross-section so as not to interfere with the central support surface (1320b-2) ^of the inner segment insulation support, when a rotational fitting end (1320b-1) of the inner segment insulating support to be subsequently coupled is rotated by a set angle and fitted to an inner locking protrusion of the window frame of the outer portion and the central portion of the window glass.