A remarkable capability of the human brain is to form more abstract conceptual representations from sensorimotor experiences and flexibly apply them independent of direct sensory inputs. However, the computational mechanism underlying this ability remains poorly understood. Here, we present a dual-module neural network framework, the CATS Net, to bridge this gap. Our model consists of a concept-abstraction module that extracts low-dimensional conceptual representations, and a task-solving module that performs visual judgement tasks under the hierarchical gating control of the formed concepts. The system develops transferable semantic structure based on concept representations that enable cross-network knowledge transfer through conceptual communication. Model-brain fitting analyses reveal that these emergent concept spaces align with both neurocognitive semantic model and brain response structures in the human ventral occipitotemporal cortex, while the gating mechanisms mirror that in the semantic control brain network. This work establishes a unified computational framework that can offer mechanistic insights for understanding human conceptual cognition and engineering artificial systems with human-like conceptual intelligence.