Objective: Multi-modal functional magnetic resonance imaging has been widely used for brain research. Conventional data-fusion methods cannot capture complex relationship (e.g., nonlinear predictive relationship) between multiple data. This paper aims to develop a neural network framework to extract phenotype related cross-data relationships and use it to study the brain development. Methods: We propose a novel method, deep collaborative learning (DCL), to address the limitation of existing methods. DCL first uses a deep network to represent original data and then seeks their correlations, while also linking the data representation with phenotypical information. Results: We studied the difference of functional connectivity (FCs) between different age groups and also use FCs as a fingerprint to predict cognitive abilities. Our experiments demonstrated higher accuracy of using DCL over other conventional models when classifying populations of different ages and cognitive scores. Moreover, DCL revealed that brain connections became stronger at adolescence stage. Furthermore, DCL detected strong correlations between default mode network and other networks which were overlooked by linear canonical correlation analysis, demonstrating DCL's ability of detecting nonlinear correlations. Conclusion: The results verified the superiority of DCL over conventional data-fusion methods. In addition, the stronger brain connection demonstrated the importance of adolescence stage for brain development. Significance: DCL can better combine complex correlations between multiple data sets in addition to their fitting to phenotypes, with the potential to overcome the limitations of several current data-fusion models.