The NMR chemical shift arising from 4d electron orbital angular momentum and 4d electron spin dipolar-nuclear Spin angular momentum interactions for a $4d^2$ system in a strong crystal field environment of octahedral symmetry has been investigated when the four fold axis is taken as the quantization axis. The NMR results are comparted with the multipolar shift at various R-values and we find that the exact results are in agreement with the multipolar shift when $R{geqslant}0.20 nm.$ We also separate the NMR shift into the contribution of the $1/R^5$ and $1/R^7$ terms. It is found that the contribution of the $1/R^5$term to the NMR shift is dominant than the contribution of the $1/R^7$ term. Temperature dependence analysis shows that the $1/T^2$ term is the dominant contribution to the NMR shift for a $4d^2$ system but the contribution of the 1/T term may not negligible. The similar results are obtained for a $4d^1$ system from the temperature dependence analysis.