How long are you mixing the icing? What recipe did you use? What kind of powdered sugar are you using?
There are as many reasons as there are recipe for the problem. You really need more information.
Make sure to use a *good brand* of sugar that is cane sugar NOT beet sugar.
Mix at least 5 minutes - even 10 is better once all the ingredients are added.
From the way your post is worded I get the feeling you are not in the U.S. Are you using powdered sugar and not granular? You mention icing is sweet - that is the nature of icing! It is meant to be sweet. You can try adding a pinch of salt - some people think that helps cut the sweetness.
What hints have you tried for solving the problem? Your post really doesn't give us many clues to be more specific.