Learning general concepts from a set of training instances has become increasingly important for artificial intelligence research on constructing knowledge-based systems. Learning strategies, according to their ways of processing training instances, can generally be divided into two classes: incremental learning strategies and batch learning strategies. Among incremental learning strategies, the 'version space' learning strategy is one of the most well-known. This learning strategy is, however, mainly applied to learning conjunctive concepts. When the concepts to be learned are disjunctive in form, the version space learning strategy will get a null version space, which cannot correctly represent the desired concepts. In this paper, we have modified the original version space strategy in order to learn disjunctive concepts. The new proposed version-space-based learning strategy, called the 'incremental multiple version spaces' learning strategy, can successfully learn disjunctive concepts in an incremental way. The correctness of the algorithm has been proven. Implementation has also been carried out on a PC/AT to verify the proposed learning strategy.