You'll see an awful lot of different putting styles and grips and types of strokes when you're watching the golf on the television. One of the guys I’d really like to look out for, Steve Stricker, has a putting stroke to really be admired and it starts by the way he grips the golf club.
It could look like a fairly traditional grip when you look at it from front up. He has one particular quirk into his left hand particularly that really puts the club and the grip in a great position to encourage him to make a pretty much a straight back and straight through stroke. It has a little curve to it but it's a very sort of consistent and very repeatable stroke and it's something I would encourage you to copy.
Basically he grips and golf club with a very straight down or even uncocked left wrist. The way I’d like to get that feeling is to point your hand straight out in front of you and make like a gun shape with the finger and then point the finger downwards and that puts the hand into an uncocked position here. If we then bring the club down and still have that uncocked arch in the back of that left wrist, the club will now run nicely through the palm of the grip rather than through the fingers as it might do in your traditional golfing grip so holding the club much more into the palm and having the cock in the wrist there but uncocked position. That then makes it very much of a straight back and a straight through putting stroke.
If you feel like you're holding the putter too much like your normal iron shots, you'd be gripping the club down too low in the fingers, having too much wrist in here and then causing yourself to have a curve in your stroke, maybe even having the heel on soled on the ground this way rather than flat with the arch in your left wrist. So if you can copy Steve Stricker's uncocked left wrist putting grip, that would help you with your putting stroke, take it more straight back and more straight through. Less wrist hinge is going to be a more consistent stroke for you.