In this paper we get the formula for the condition number of the $W$-weighted Drazin inverse solution of a linear system $WAWx=b$, where $A$ is a bounded linear operator between Hilbert spaces $X$ and $Y$, $W$ is a bounded linear operator between Hilbert spaces $Y$ and $X$, $x$ is an unknown vector in the range of $(AW)^D$ and $b$ is a vector in the range of $(WA)^D$.