Mean-field homogenization methods relying on the solution of Eshelby's inclusion problem do not provide accurate predictions when the interaction among reinforcements becomes significant, or in the inelastic response regime when the shape of the reinforcement has a high aspect ratio. Herein, we propose a combined theoretical and data-driven approach in which a homogenization method is followed by transfer learning to enhance the prediction of the nonlinear mechanical response of particle/short fiber-reinforced composites. We trained a deep neural network (DNN) with a massive stress-strain curve dataset of the composites subjected to uniaxial and cyclic loading in the elasto-plastic regime based on the adaptive incrementally affine homogenization method; then, we fine-tuned the pre-trained DNN via transfer learning with a relatively small dataset based on timeconsuming three-dimensional (3D) finite element analyses (FEA). The transfer learning approach exhibited better predictive performance than the DNN directly trained only with the FEA dataset did, for a wide range of reinforcement volume fractions and shapes. With transfer learning, the DNN exploits the knowledge learned from the homogenization theory to perform new learning tasks on small datasets from 3D FEA. The proposed approach can be extended to other composite analyses requiring excessive time and cost for large datasets.