The connectional map of the baby brain undergoes dramatic changes over the first year of postnatal development, which makes its mapping a challenging task, let alone learning how to predict its evolution. Currently, learning models for predicting brain connectomic developmental trajectories remain broadly absent despite their great potential in spotting atypical neurodevelopmental disorders early. This is most likely due to the scarcity and often incompleteness of longitudinal infant neuroimaging studies for training such models. In this paper, we propose the first approach for progressively predicting longitudinal development of brain networks during the postnatal period solely from a baseline connectome around birth. To this end, a supervised multi-regression sample selection strategy is designed to learn how to identify the best set of neighbors of a testing baseline connectome to eventually predict its evolution trajectory at follow-up timepoints. However, given that the training dataset may have missing samples (connectomes) at certain timepoints, this may affect the training of the predictive model. To overcome this problem, we perform a low-rank tensor completion based on a robust principal component analysis to impute the missing training connectomes by linearly approximating similar complete training networks. In the prediction step, our sample selection strategy aims to preserve spatiotemporal relationships between consecutive timepoints. Therefore, the proposed method learns how to identify the set of the local closest neighbors to a target network by training an ensemble of bidirectional regressors leveraging temporal dependency between consecutive timepoints with a recall to the baseline observations to progressively predict the evolution of a testing network over time. Our method achieves the best prediction results and better captures the dynamic changes of each brain connectome over time in comparison to its ablated versions using leave-one-out cross-validation strategy. (C) 2020 Elsevier B.V. All rights reserved.