Our aim was to improve the accuracy of classifying x-ray mammographic breast densities. The histogram approach using the neural network was used for the purpose of constructing a flexible system. In this study the phantom of the synthetic breast-equivalent resin material for the process of the A/D conversion of mammograms was employed. The digital values can offset the difference in characteristics between the mammography system, the unit, etc. Furthermore the features of our system use the neural network, and then tune the neural network by the histogram of the digital values and by the radiologists' and expert mammographers' assessment ability. Although there was an observer's bias, our system was able to classify the breast density automatically according to that observer. This is only possible if the observer has been trained to some extent and is capable of maintaining an objective assessment according to the assessment criteria.