Concept-cognitive learning has been widely used in simulating the human brain to learn concepts. However, the existing concept-cognitive learning models mainly focused on how to acquire knowledge and its properties, but not how to solve the problems. The underlying skills for solving problems are ignored in the cognitive learning process. Indeed, a concept-cognitive learning process is always accompanied with problem solving and skill learning, and the skills are necessary for solving problems. Knowledge space theory is an effective mathematical analysis approach for knowledge assessment. Nevertheless, the existing learning paths for skill were evaluated by constructing the concept lattice, which is a NP hard problem. To overcome these limitations and problems, a novel concept-cognitive learning model from a perspective of competences is proposed. Firstly, knowledge and skills can be represented by item sets and skill sets. And a good semantic explanation between knowledge and skills is provided by a competence-based concept, which presents that one can acquire the most knowledge with the least amount of skills. Secondly, a competence-based concept-cognitive learning model and its properties are put forward to describe the concept-cognitive learning through skills. Moreover, by analyzing the sufficient and necessary relationship between skills and knowledge, a competence-based information granule structure is constructed. Finally, a transformation method of information granules is proposed to convert a general information granule into sufficient and necessary competence-based information granules (i.e., competence-based concepts). And the experimental results of UCI data sets show that the competence-based concept-cognitive learning model is feasible and effective.