  In this article, we consider a semi discrete finite difference scheme for a
degenerate parabolic-hyperbolic PDE driven by L\'evy noise in one space
dimension. Using bounded variation estimations and a variant of classical
Kru\v{z}kov's doubling of variable approach, we prove that expected value of
the $L^1$-difference between the unique entropy solution and approximate
solution converges at a rate of $(\Delta x)^\frac{1}{7}$, where $\Delta x$ is
the spatial mesh size.
