The adjective foolproof means infallible or, more literally, impervious to the incompetence of fools. Just as a bulletproof vest makes one invulnerable to bullets, a foolproof plan is designed to be invulnerable to fools. Foolproof is usually one word, without a hyphen (though the hyphenated form, fool-proof, is not uncommon).
The word is occasionally misspelled full-proof. There are arguments to be made in favor of this spelling (see the comments below for a couple of them), and of course anyone who likes it is free to use it, but it is not the conventional spelling (i.e., the more common one and the one listed in dictionaries) and is likely to be seen as a misspelling by some readers.
The public knows that no security system can be foolproof, but some acknowledgement of accountability is warranted nonetheless. [Milwaukee Journal-Sentinel]
This is not foolproof from a security standpoint since the malicious individual could simply configure their computer with an IP address on the network. [Digital Evidence and Computer Crime, Eoghan Casey]
Apparently, DNA testing was seen as so foolproof that alibis didn’t count. [Herald Sun]
It can be tweaked according to the talent at hand, but nothing is foolproof, especially with young players. [Sports Illustrated]
One foolproof method of contraception is sterilization. [Life: The Science of Biology]
Here, he shows a simple roasting technique that’s both foolproof and infinitely adaptable. [Globe and Mail]