A sprocket assembly for a bicycle includes a sprocket body formed by a plurality of sprocket rings, and a collar mounted in the sprocket body. The sprocket body has a first side provided with a fitting portion and a second side provided with a mounting tube. The collar is received in the fitting portion of the sprocket body. The sprocket rings have different inner diameters so that the sprocket rings are arranged to have a stepped inner periphery, and have different outer diameters so that the sprocket rings are arranged to have a stepped outer periphery. Thus, the collar is separated from the sprocket body and is made independently so that the collar can be worked easily and quickly to fit shafts of different specifications and sizes and to fit the sprocket body of different specifications and sizes.