Model-based techniques for reactive systems generally assume the availability of a state machine that describes the behavior of the system under study. However, the assumption may not always hold in reality. Even the assumption holds, the state machine could be invalidated when the system evolves. This triggers the study of adaptive model checking, which necessitates an iterative construction of a state machine for a system. In this paper, we propose a dynamic learning approach based on genetic algorithm to iteratively generate a finite-state automaton from a given system. In view of the fact that modern systems are apt to change, our algorithm postpones expensive equivalence checking until the associated accuracy is required for the verification of some properties. We explain in details the core learning process of our algorithm, including encoding the model and its synthesis from a given training set. Experimental results show that our algorithm is scalable in memory consumption. Dynamic model learning technique helps model checking of evolving reactive system.