I use a potato peeler.   

Some people find the round shape a challenge for cutting swedes/turnips. Once you have a flat surface cut to provide a firm surface, its easier. I use a wavy (krinkle type) vegetable cutter - the type I have is designed to allow me to come down on it with a bit of force and cut the swede in any size chunks. It works for me. (I even suspect smaller chunks may be easier to peel- but I peel first.