Call of Cthulhu was suggested by others - but it's too lethal, in my opinion, if you're trying to emulate the show at all. Also, the insanity mechanics don't seem to apply well, and it doesn't have options for different power levels of characters.
While nothing is stopping you from tweaking Call of Cthulhu to taste, these are some of the reasons I'd go with BRP (the gold book) instead of straight-up Call of Cthulhu.
The BRP gold book is full of options and optional rules and is designed to be adjusted. It has options to adjust the lethality, options for something like "fate points", sanity rules are optional/adjustable, it has options for power levels, et cetera. You get the benefits of Call of Cthulhu's base d100 system and a whole host of predefined options to adjust the rules to suit the kind of gameplay you want. The only real downside, to my mind, is that you need to define what options you're going to use instead of having everything "preset" for you.