A golf putter head having a vertically curved putter face with multiple horizontal contact facets. The face has a vertical radius of curvature that is at least 2 inches and no more than 3.5 inches. The face includes a plurality of horizontal contact facets that are vertically curved to match the vertical radius of curvature. The contact facets, along with the radius of curvature, ensure that no more than two of the horizontal contact facets contact the golf ball when struck by the putter head at a speed of less than 15 miles per hour. The putter produces a horizontal linear contact, or impact, geometry that compensates for misdirection of the path of the putter head throughout the stroke of the putter head. At least one of the horizontal contact facets is located at an elevation above the center of curvature and at least one is located below.