Epistemic closure principle is an important topic in the theory of knowledge, and logic is the basic tool for the discussion of this topic. Logical omniscience problem is the result of epistemic closure principle as an initial axiom in the systems of epistemic logic, which both presuppose idealized cognitive subject. There are some differences, i.e. epistemic closure principle is the cognitive group, while the logical omniscience problem is relative to the cognitive subject who is characterized by epistemic logic system. Because of the presupposed idealized cognitive subject, the subjects cognitive ability is the absolute correctness, which can lead to that epistemic closure principle is failure and the logic omniscience subject is not intuitive. From this point of view, the analysis of epistemic closure principle contributes to the reason analysis of the logical omniscience, and the solution to the logical omniscience also contributes to the defence of epistemic closure principle.