A novel molecular connectivity index, denoted as (m)chi ' and based on the adjacency matrix of molecular graphs and novel atomic valence connectivities (delta(i)') is proposed. The index is successfully applied to predict the molar diamagnetic susceptibilities of organic compounds. A good quantitative structure-property relationship (QSPR) model for molar diamagnetic susceptibilities can be constructed from (0)chi ', (1)chi ', and (2)chi ', using a multivariate linear regression (MLR). The correlation coefficient (r), standard error, and average absolute deviation (AAD) of the MLR model are 0.9917, 5.42 cgs, and 4.14 cgs, respectively, for 720 organic compounds. Cross-validation through the use of the leave-one-out method demonstrates that the MLR model is highly reliable. Using the MLR model, the AAD of the predicted values of molar diamagnetic susceptibilities of another 361 organic compounds (test set) is 4.69 cgs. The result shows that the current method is more accurate than literature methods for estimating the molar diamagnetic susceptibility of an organic compound. The MLR method can provide an acceptable model for the prediction of the molar diamagnetic susceptibilities of the organic compounds.