Breast cancer is one of the most common cancers and has high morbidity and mortality worldwide, posing a serious threat to the health of human beings. The emergence of microcalcifications (MCs) is an important signal of early breast cancer. However, it is still challenging and time consuming for radiologists to identify some tiny and subtle individual MCs in mammograms. This study proposed a novel computer-aided MC detection algorithm on the full field digital mammograms (FFDMs) using deep convolution neural network (DCNN). Firstly, a MC candidate detection system was used to obtain potential MC candidates. Then a DCNN was trained using a novel adaptive learning strategy, neutrosophic reinforcement sample learning (NRSL) strategy to speed up the learning process. The trained DCNN served to recognize true MCs. After been classified by DCNN, a density-based regional clustering method was imposed to form MC clusters. The accuracy of the DCNN with our proposed NRSL strategy converges faster and goes higher than the traditional DCNN at same epochs, and the obtained an accuracy of 99.87% on training set, 95.12% on validation set, and 93.68% on testing set at epoch 40. For cluster-based MC cluster detection evaluation, a sensitivity of 90% was achieved at 0.13 false positives (FPs) per image. The obtained results demonstrate that the designed DCNN plays a significant role in the MC detection after being prior trained.