The Barbell having parallel forearm engaging bar is an accessory for use with a barbell. The accessory can be installed upon an existing barbell and includes a second bar that is parallel with the barbell by a distance defined by a cross brace. The second bar features a paid of foam pads that engage the forearm of an end user so as to minimize wrist strain during a curling exercise with the barbell. The accessory includes a clamp assembly that enables the accessory to be installed and/or removed from the barbell.