Granular computing (GrC) and two-way concept learning (TCL) are influential studies of knowledge processing and cognitive learning. A central notion of two-way concept learning is learning concepts from an arbitrary information granule. Although TCL has been widely adopted for concept learning and formal concept analysis in a fuzzy context, the existing studies of TCL still have some issues: the sufficient and necessary granule concept is only obtained from the necessary granule or sufficient granule concept; and the cognitive mechanism ignores integrating past experiences into itself to deal with dynamic data. Meanwhile, concept-cognitive learning (CCL) method still faces challenges, such as incomplete cognitive and weak generalization ability. This article proposes a novel two-way CCL (TCCL) method for dynamic concept learning in a fuzzy context for these problems and challenges. Unlike TCL, fuzzy-based TCCL (F-TCCL) is more flexible and less time consuming to learn granule concepts from the given clue, and meanwhile, it is good at dynamic concept learning. Moreover, we design a fuzzy-based progressive learning mechanism within this framework under the dynamic environment. Some numerical experiments on public datasets verify the effectiveness of our proposed method. The considered framework can provide a convenient novel method for researching two-way learning and CCL.