Norman Baker quit last night complaining that working under Home Secretary Theresa May was like "walking through mud".
He accused her of viewing coalition colleagues as "a cuckoo in the nest rather than part of government".
"They have looked upon it as a Conservative department in a Conservative government, whereas in my view it's a Coalition department in a Coalition government," he told the Independent.
"That mindset has framed things, which means I have had to work very much harder to get things done even where they are what the Home Secretary agrees with and where it has been helpful for the Government and the department.
"There comes a point when you don't want to carry on walking through mud and you want to release yourself from that."
Premier's Political Editor, Martyn Eden
Norman Baker and Home Secretary Theresa May fell out over Mr Baker's advocacy of decriminalising drug possession.
The Home Office has a zero-tolerance of drugs but Mr Baker has been impressed by Portuguese experience. They treat drug possession as a health issue not a criminal one and possession of small quantities is no longer a criminal offence.
He wants to Britain to adopt this policy but Mrs May and the Prime Minister do not.
Mr Baker's resignation is a personal decision and not a sign of the Coalition breaking up.
Deputy Prime Minister Nick Clegg said he was regretful at the loss of "one of the most effective ministers" in the Government but said he "fully" understood why he was going.
Mr Baker's formal resignation letter said: "You will recognise that it has been particularly challenging being the only Lib Dem in the Home Office, which I see a newspaper the other day likened to being the only hippy at an Iron Maiden concert.
"Despite these challenges, I am pleased with what I have been able to achieve, not least to have been the first minister with responsibility for drugs to have put prejudice aside and published an evidence-based approach to this important issue, despite repeated Conservative efforts to block release."
A Lib Dem spokesman said a replacement would be announced "in due course".