A sleeve bracket assembly has a frame and multiple first sleeve mounts. The frame has a first sleeve track having a groove. Each first sleeve mount has a base and a hollow positioning button protruding from a top surface of the base and having a retractable protrusion or a flange. The cross section of the base or the positioning button of each first sleeve mount is round, so sleeves can be rotated. The protrusions and the flanges can securely position the sleeves. Accordingly, the sleeve bracket assembly can position the sleeves firmly and also allow the sleeves to be rotated.