Longitudinal magnetic resonance imaging (MRI) has an important role in multiple sclerosis (MS) diagnosis and follow-up. Specifically, the presence of new lesions on brain MRI scans is considered a robust predictive biomarker for the disease progression. New lesions are a high-impact prognostic factor to predict evolution to MS or risk of disability accumulation over time. However, the detection of this disease activity is performed visually by comparing the follow-up and baseline scans. Due to the presence of small lesions, misregistration, and high inter-/intra-observer variability, this detection of new lesions is prone to errors. In this direction, one of the last Medical Image Computing and Computer Assisted Intervention (MICCAI) challenges was dealing with this automatic new lesion quantification. The offers an evaluation framework for this new lesion segmentation task with a large database (100 patients, each with two-time points) compiled from the OFSEP (Observatoire français de la sclérose en plaques) cohort, the French MS registry, including 3D T2-w fluid-attenuated inversion recovery (T2-FLAIR) images from different centers and scanners. Apart from a change in centers, MRI scanners, and acquisition protocols, there are more challenges that hinder the automated detection process of new lesions such as the need for large annotated datasets, which may be not easily available, or the fact that new lesions are small areas producing a class imbalance problem that could bias trained models toward the non-lesion class. In this article, we present a novel automated method for new lesion detection of MS patient images. Our approach is based on a cascade of two 3D patch-wise fully convolutional neural networks (FCNNs). The first FCNN is trained to be more sensitive revealing possible candidate new lesion voxels, while the second FCNN is trained to reduce the number of misclassified voxels coming from the first network. 3D T2-FLAIR images from the two-time points were pre-processed and linearly co-registered. Afterward, a fully CNN, where its inputs were only the baseline and follow-up images, was trained to detect new MS lesions. Our approach obtained a mean segmentation dice similarity coefficient of 0.42 with a detection F1-score of 0.5. Compared to the challenge participants, we obtained one of the highest precision scores (PPVL = 0.52), the best PPVL rate (0.53), and a lesion detection sensitivity (SensL of 0.53).