Chemical shifts of some reduced symmetry peripheral fused-ring-substituted phthalocyanines, namely Zn3B1N, Zncis2B2N, Zntrans2B2N, Zn1B3N and Zn3B0N, have been calculated at density functional B3LYP level using the gauge-independent atomic orbital (GIAO) method. The geometries were optimized using the 6-31G(d) basis set and the following NMR calculations were performed using 6-31G(d) and 6-311G(d,p) basis sets, respectively. The calculated NMR shielding tensors and chemical shifts are compared with previous experimental results. The chemical shifts are assigned according to the calculated data and satisfying results are obtained. The NMR shielding tensor simulation of Zn3B0N has been raised as a significant theoretical topic.