Concept-cognitive learning is an emerging area of cognitive computing, which refers to continuously learning new knowledge by imitating the human cognition process. However, the existing research on concept-cognitive learning is still at the level of complete cognition as well as cognitive operators, which is far from the real cognition process. Meanwhile, the current classification algorithms based on concept-cognitive learning models (CCLMs) are not mature enough yet since their cognitive results highly depend on the cognition order of attributes. To address the above problems, this article presents a novel concept-cognitive learning method, namely, stochastic incremental incomplete concept-cognitive learning method (SI2CCLM), whose cognition process adopts a stochastic strategy that is independent of the order of attributes. Moreover, a new classification algorithm based on SI2CCLM is developed, and the analysis of the parameters and convergence of the algorithm is made. Finally, we show the cognitive effectiveness of SI2CCLM by comparing it with other concept-cognitive learning methods. In addition, the average accuracy of our model on 24 datasets is 82.02%, which is higher than the compared 20 classification algorithms, and the elapsed time of our model also has advantages.