Finding the exact spanning ratio of a Delaunay graph has been one of the longstanding open problems in Computational Geometry. Currently there are only four convex shapes for which the exact spanning ratio of their Delaunay graph is known: the equilateral triangle, the square, the regular hexagon and the rectangle. We add a fifth convex shape by proving the exact spanning ratio of the parallelogram Delaunay graph. The worst-case spanning ratio is exactly \( \frac{\sqrt{2}\sqrt{1+A^2+2A\cos (\theta _0)+(A+\cos (\theta _0))\sqrt{1+A^2+2A\cos (\theta _0)}}}{\sin (\theta _0)}, \) where A is the aspect ratio and \(\theta _0\) is the non-obtuse angle of the parallelogram.