Which is correct?

1. I am taller than " her" .

2. I am taller than " she" .

Hello, Joy Lin-- welcome to English Forums.

Both sentences are fine in appropriate circumstances. When we are speaking, we often use #1, but when you are writing, you should use #2, because it is more formally correct: it means I am taller than she is.
good job, micawber. nice to know that, I didn't know.