A scream may sound awful to you, but to your baby it's just another way to flex his vocal cords. Many babies go through a phase during which they scream loud and long, sometimes just for the fun of it. (Lucky you!) Have patience — these screaming episodes soon become less intense and less frequent.
Usually the goal of screaming is to get something from you. Your baby may be frustrated -- babies interpret getting what they want as a sign of your love, so not getting their way can be very upsetting for them. Of course, a scream can also indicate that your baby is hurt or ill.
Whatever you do, don't scream back. Babies imitate their parents' behavior, so trying to demonstrate how unpleasant screaming sounds will only backfire.
Try to keep your cool. Calmly meet your baby's need as best you can. Better still, aim to prevent at least some of the screaming before it starts by paying more attention to your baby before he reaches his "breaking point." Make sure his basic requirements are met (he's not hungry, tired, cold, etc.), and give plenty of nonverbal physical signs of affection, like holding his hand.
~ Courtesy of Baby Center