Putter head 2 having a head main body 4 constructed with a metal, and a member having low specific gravity 6 constructed with a material having a specific gravity lower than that of the metal constructing the head main body 4. The member having low specific gravity 6 is provided on the sole surface 16 side of the head main body 4. At least a part of the sole surface 16 is constructed with the member having low specific gravity 6. Preferably, the head main body 4 has a hollow part t. Preferably, the center of gravity g2 of the member having low specific gravity 6 is located to get closer to the face side than the center of gravity g1 of the head does. The golf putter according to the present invention has the putter head 2, a shaft 3, and a grip. The present invention provides a golf club head for a putter and a golf putter which achieve favorable rolling.