Stress

[evilhui]

I felt afraid when my teacher is looking beside me. The teacher
did not scolded me or anything. My hands just trembled when i am
playing the piano. But when i am practicing, the feeling is not the
same. I talked to myself how to do this, do that and my scareness
just gone like this. Even i talk to myself when teacher is beside me,
I still have this afraidness. How to overcome this? My teacher said
I am improving.

[Hmoll]

So, you get nervous when someone, who is an expert at playing the piano and evaluating your strengths and weaknesses, is sitting right next to you watching your every move while you are playing?

Believe it or not, this is not an uncommon reaction. Two things I have accepted a long time ago: 1) I get a little nervous at lessons, and 2) I never play as well in lessons as I do when I practice.
If your nervousness is excessive and is ruining the lessons for you, you should discuss it with your teacher.
Sometimes just saying "I don't know why I get nervous in my lessons," is enough to clear the air.  Or, you might want to have a more detailed discussion with your teacher about the whole concept of nerves, performance anxiety, etc.

[NetherMagic]

evilhui i have those feelings too

just one thought to make it less fearful for you at the lessons, make sure you communicate with the teacher like your friend not your teacher.  My previous teacher, whom was good at piano but I didn't like her, because she enver understood what problems I had.  Just make sure you keep in mind that your teacher's there to help you and not criticize you (well maybe a little but it's a lot more different from judges) and that if you don't play well she doesn't look good either, hehe  

newayz good luck