The article aims to analyze and reconstruct John Stuart Mill's position on the problem of induction. We show that Mill despite being aware of Hume's objections, does not refer to them mainly because for him the justification of induction is possible. The main hypothesis will be proved by two theses: The first, refers to the avoidance of circular reasoning on the justification of inductive inference; and the second, refers to the type of inductions supporting the principle of regularity: Inductions by simple enumeration.