Something is making you more nervous in this situation than normal day=to=day conversation with your boss. You need to identify what that something is to come up with the best strategy for fixing the problem.
You say you know you are prepared but your actions speak otherwise even if you don't intend them to. So maybe changing exactly how you are prepared and how you do the presentation will help. For instance, are you going into the conversation with written notes? How about a Power Point presentation? If you present your plan using a formal presentation, you can spend a lot of the time looking at the screen and not the person which will help the eye contact problem. If you have written notes you know you won't forget something.
If is truly is not preparedness, then some other issues might be:
Your boss doesn't provide any signals that let you know if you are doing well or poorly. Therefore talking to him makes you feel uneasy since you can't tell how he is reacting. I had this problem when I was first in the work place and the trick is to ask him leading questions to get the feedback rather than relying on him to give it to you when it is not his natural style. You can also assume with these sorts of people that no news is good news. If you aren't getting bad feedback, assume you are doing well. Feeling that he is going to respond positively to what you have to say will make it easier to say it.
Another reason for this sort of nervousness is that you feel you are going to tell him some news he won't want to hear. So if you think the project plan you have will be unacceptable to the manger, decide why and think of reasons to mitigate the problem. For instance, it is harder to go to the boss with a problem than just to say hi. However, if you go to him with a problem and a proposed solution, then you will feel more confident and he will be happier than just finding out about a problem.
Another possibility is psychological. People who have been abused by authority in the past, tend to have difficulty speaking to authority figures later in life. Not being able to make eye contact is a possible sign of this. This is because the abused person doesn't internally have a basic level of trust that the non-abused person has. The best solution here is to seek treatment.