I too have this issue
The fear of being told '
hey, you creep me out with your stare', or '
dude, you are looking at me funny'
It's a confidence thing, and I am slowly getting over my fear
Here's a bunch of stuff I try
I try and turn it around. Instead of worrying '
what if I'm looking at people funny', think to yourself, '
If you can't handle the way I look at you - then it's your problem, not mine'. This is not to say be aggressive, far
far from it, but instead of battering yourself over the head with it all the time, try looking at it as a positive. For example, I imagine that holding someone's gaze all the time whilst speaking with them, would prompt them to say in conversation with other; 'You can tell he's a really confident person by the way he looks at you - always with the eye contact'
I suck it up, I look them in the eye and think to yourself '
You look away!' Give yourself a challenge, but be careful not to come across as some
leaning forward bulging eyeball starting monster. I'm talking about taking off the wheel retainers, the arm bands for swimming, and telling yourself '
I'm as good as anyone in this room - better even!' But always tempered with love and caring for your fellow human being.
In fact, you are not so much as challenging them, you are more challenging yourself. Think of the person you are speaking with, as someone who has been very kind enough to lend you their eyes so you can practice your 'look'.
And one great tip that helps me;
listen intently to what the other person is saying to you.
All too often I find I'm just nodding and not really hearing anything because I'm so focused on the whole 'eyeball' thing. The brain can't devote 100% focus to two things at once (well, not mine at least

), so go for the '
I'm really interested and I'm listening to you' tactic rather than the '
Uh on, am I looking at them in some weird way?'
Go on youtube, put in this search 'Can't make eye contact' or 'difficulty looking people in the eye' and you'll get some advice. But the main reason I do this, is to use the person speaking as my training partner. I listen to them and I maintain eye contact whilst pretending they are in the room with me and not thousands of miles away. It's great training. You can do this with news presenters on the T.V, or even yourself in the mirror.
The reality is, it's very difficult to 'look' at someone in any weird way unless you are bulging your eyes or flat out starting at them, non blinking.
The problem is not our eyes, it's our mind
Life is 99% mental conditioning. The other 1% is realising it's 99% mental conditioning.
It's a confidence thing. Time to come out of our shells and start being more positive about ourselves.
I'm awesome! How are you?