A curb forming machine for use by a single operator to form curved curbing includes a single rotatable curb-forming roller, a handle assembly for pulling and maneuvering the roller, and a motor for rotating the roller. The roller includes a generally cylindrical body, a neck at one end of the body, and a shaping surface, all of which are coaxial. The motor rotates the roller so that the lower periphery of the roller moves toward the direction of pulling to shape and smooth wet concrete into curbing. An overflow guard prevents wet concrete from flowing over the roller onto the finished curb, and an alignment device extends outwardly from the roller to contact a form member. A curb forming method includes pulling and steering such a roller around a curved form, including around tight curves in the form.