In 1936, Lee Falk colored the Phantom's costume gray. Of course, that was for a daily, black and white newspaper strip, so it could have been any color. Falk had actually intended the costume to be gray. He had even toyed with naming his new mystery man "The Gray Ghost".
It wasn't until 1939, when King Features began running a color, Sunday strip of the Phantom that the suit was depicted as purple. It isn't recorded why the colorists chose purple, but Falk continued to describe the costume as gray within the text of the strip. Eventually, Falk gave in and let it be purple.
In some countries, the Phantom's costume is depicted as red (in Italy, Turkey and South America) or blue (In Norway, Sweden and Finland).