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Data-driven methods have attracted increasingly more attention in materials research since the advent of the material genome initiative. The combination of materials science with computer science, statistics, and data-driven methods aims to expediate materials research and applications and can utilize both new and archived research data. In this paper, we present a data driven and deep learning approach that builds a portion of the structure–property relationship for polymer nanocomposites. Analysis of archived experimental data motivates development of a computational model which allows demonstration of the approach and gives flexibility to sufficiently explore a wide range of structures. Taking advantage of microstructure reconstruction methods and finite element simulations, we first explore qualitative relationships between microstructure descriptors and mechanical properties, resulting in new findings regarding the interplay of interphase, volume fraction and dispersion. Then we present a novel deep learning approach that combines convolutional neural networks with multi-task learning for building quantitative correlations between microstructures and property values. The performance of the model is compared with other state-of-the-art strategies including two-point statistics and structure descriptor-based approaches. Lastly, the interpretation of the deep learning model is investigated to show that the model is able to capture physical understandings while learning.