My old cat is jelouse of my new kitten !?

Okay, well I've had my cat Spike for 2 and a half years now. But we recently got a new kitten about 2 or 3 weeks ago. Spike is an outdoor cat, he comes in for about 30 minutes a day to eat and give us some affection. He is a brutal hunter, kills squirells,birds,mice,EVERYTHING. Whenever he comes in, we have to put our new kitten,Mitch, in a different room. We have showed Mitch to Spike about 3 times, and he growls and hisses at him everytime, and once even tried to attack him! When winter comes around, Spike will stay in alot more often. Spike feels replaced ! I dont want Spike to KILL Mitch(he will if he gets the chance) and I dont want Spike to run away !?