The Bears scored 265-7in their alloted fifty overs with Tim Ambrose hitting 58 and Darren Maddy completing his half century.
Leicestershire were skittled out of 206 to give Warwicks a win by 59 runs with Steyn taking 5-29.
Ian Bell managed to score only three in his second innings at the first test at Lords. Monty Panesar had helped to skittle out the West Indies for 437.
England knocked up 284-8 before declaring and setting the visitors 401 for victory. At the close,the West Indies were 7-0.