We developed a new type of polymer descriptor based on Extended Connectivity Fingerprints. The number densities, that are substructure numbers divided by the number of atoms in a polymer model, were employed. We found that this approach is superior in accurately predicting linear polymer properties, compared to the conventional approach, where just the substructure numbers are used as descriptors. In addition, dimension reduction and multiple replication of repeat unit were found to improve prediction accuracy. As a result, the novel descriptor based on the Extended Connectivity Fingerprints with machine learning approaches was found to achieve accurate prediction of the refractive indices of linear polymers, which is comparable to that by ab initio density functional theory. Although process-dependent properties such as mechanical properties were difficult to predict, the present approach was found to be applicable to prediction of substructure-dependent properties, for example, optical properties, thermal stabilities.