A golf club putter head includes a faceplate groove pattern configured to provide the putter head with an elevated center of gravity. In one preferred form, a club head body defines a faceplate having at least one and preferably multiple elongated grooves formed therein to extend generally in a heel-to-toe direction, with at least one groove positioned above a vertical mid-point of the club head body. The groove depths progressively increase in a top-to-bottom direction so that the putter head center of gravity is elevated to a position spaced above the vertical mid-point of the club head body. When striking a golf ball, the elevated center of gravity functions to minimize initial ball skidding and to promote early smooth ball roll toward a target such as a cup on a golf green.