ESPN Demands $300k from Erin Andrews' Stalker

ESPN believes the man who peeped Erin Andrews isn't done paying for his crimes -- the sports giant wants more than $300k from Michael David Barrett for the mess he caused the network.

During the time of the peeping, Andrews was working as a reporter for ESPN -- and according to federal documents filed yesterday in California, the net claims they had to cough up a ton of cash to pay for extra security for Andrews.

In the docs, ESPN also claims they incurred losses "from assisting the government in its investigation."

ESPN is demanding that Barrett pay back every cent of the $327,442.27 they ultimately spent on the Andrews situation.

Barrett -- who pled guilty to stalking Andrews last year -- began serving a 30 month sentence on May 3.