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Ch. S. Peirce recognizes induction as one of the three moments of the scientific method. This means that he thought that the induction was, in a way, justified. In this paper I intend to review what Peirce’s response might be to the traditional problem of induction, namely, the problem of justifying a general principle of inductive inferences. This principle is traditionally characterized as the Principle of uniformity of nature (PU). Particularly, then, I am interested in evaluating Peirce’s opinion regarding the justification of a PU version, namely, the Principle of regularity of nature (PR). The work is composed of three sections, the first will present a version of the argument that gives rise to the traditional problem of induction; in the second, a reconstruction of the characterization of Peirce’s PR will be offered; and in the third, it will be reviewed in which way for Peirce the PR could be justified—which would seem to solve Hume’s problem; finally, in the fourth section, as a conclusion, a brief evaluation of this possible answer of Peirce to Hume’s problem will be offered.