A sleeve bracket assembly includes a rail base, a positioning board and multiple positioning mounts. The rail base includes two side boards and a connecting seat connecting with the side boards. Each side board has a sliding rail protruding from an inner surface of the side boards. The positioning board is integrally formed with the sliding rail. The positioning mounts are rotatably and movably mounted in the rail base and abut the positioning board. The positioning mounts are positioned between the positioning board and the rail base. When no external force is applied, the positioning mounts will not move or rotate.