We present a finite difference solution for a parabolic weakly singular partial integro differential equation with multi-point nonlocal boundary conditions. The singularity in the considered equation is removed using Taylor's approximation. The stability analysis for the implicit and explicit finite difference schemes are studied. Then, the effect of the parameter of multipoint nonlocal boundary conditions on the eigenvalues of the transition matrix is studied via spectral analysis. We conclude this paper with the results of a numerical experiment to show the effciency of the technique.