'Believe you me' is an archaic or odd way of saying it, but some people do say it like that. It is a command, 'Believe me!/trust me'.

Welcome, Akane. You are right, that's a US specific usage, or an "Americanism" as it used to be called once.

>Som Thank you for the explanation! I watch a drama from the US and this expression came up three times. I was really wondering why they use ‘believe me’ in such way. Now I got it.

That's not a grammatically correct use but a perfectly valid coloquial one. What it means is either "please do believe me" or "you must believe me" or even "you had better believe me". It conveys a stronger need to believe the speaker than just a simple statement.