This question already has an answer here:
Is it correct to say "between you and me" or "between you and I"?
I am not a native English speaker, so please bear with me.
Between you and me is the correct usage.
This is an English teacher's classic. Because the phrase occurs after the preposition between, you have to use the object pronoun me rather than the subject pronoun I.
I even found a proper source to back me up. But, this one is a classic.
Just between you and I, the answer depends on whether or not you're in school, or writing for a boss, or writing for yourself:
For decent info that's easy to understand, you might be interested in a usage dictionary, such as Merriam-Webster's Dictionary of English Usage. In that way, you can see the involved style issues and other stuff. (The entry is "Between you and I" in MWCDEU.)
As to grammar: Usage similar to "between you and me" is part of today's standard English, while the evaluation on usage similar to "between you and I" is perhaps not so clear-cut. According to the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL), they think that usage similar to "between you and I" should be considered a variety of today's standard English. CGEL, page 463,
EDITED: Since a recent comment brought up the issue of hypercorrection, and since an old thread has also been brought up (one that has plenty of bad info in it), this following info might be helpful.
Some more info from CGEL, page 463,
There is more info on page 463, which I've omitted from the excerpts, that is related to this issue of hypercorrection. (But my fingers are tired now.)