A bicycle rim brake assembly includes a fastening shaft, a mounting part, a pair of brake arms and a pair of brake shoe attaching parts. The fastening shaft extends in an axial direction and is configured for attachment to a portion of a bicycle frame adjacent to the bicycle wheel. The mounting part includes a fastening portion that is configured such that the fastening shaft extends through the fastening portion. The mounting part and the fastening portion are movable between a plurality of mounting positions relative to the fastening shaft along a first direction that intersects the axial direction. The brake arms are supported in a freely pivotal manner on an outer perimeter of the mounting part. The brake shoe attaching parts are provided on respective ones of the brake arms.