The answer here is pretty straight up, yes they do have first class travel category that comes along with numerous premium benefits which you can avail or say enjoy while onboard on southwest first class category. Passengers having SW booking can get hold of all the luxury items that being offered by the airlines in the first class flights. For further information related to Southwest Airlines first class, or to know how it is traveling in the first class category of Southwest Airlines, reach out to our customer service agent for better knowledge and understanding related to first class SW booking.