A three-dimensional asymptotic density-potential relation is established for a spiral galaxy with a disk of finite thickness. This relation is accurate to the order /kr/−3, where k is the radial wave number and r is the radial distance from the center of the galaxy. In the case of small disk thickness, some simpler and more explicit relations are obtained with the accuracy of order /kr/−2, which is usually sufficient for the discussion of spiral mode. A density-potential relation, accurate to the order /kr/−3, is also obtained for the zero-thickness disk. To the order /kr/−2, this relation reduces to that given earlier by Bertin and Mark (1979), but the present derivation is simpler. The dynamical effect of the density-potential relation for a disk of finite thickness is investigated in Yue (1981).