This paper aims to shed light on Henri Poincaré’s intuitionism. Today, the intuitionistic philosophy of mathematics is usually associated with L.E.J. Brouwer and the idea of expelling the proofs which rest on the law of excluded middle from mathematics. There is a widespread supposition that intuitionists argue that there is a certain error in our standard way of doing mathematics and that a radical change in mathematics is needed. It is interesting to note, however, that Immanuel Kant, who was the first philosopher to relate mathematics to the intuitions of the human being, did not maintain such an argument and he used the term intuition in a different sense than what is generally understood today. This is also true of Poincaré, who made a significant revision to Kant’s philosophy of mathematics and who is usually regarded as a pre-intuitionist or a semi-intuitionist. Some philosophers, such as Warren Goldfarb, rightly argued that Poincaré’s concern in invoking intuition was to explain the psychological aspect of mathematical thinking. It is argued in this paper that this psychological aspect was not the whole point of Poincaré’s intuitionism as there is a notion of a pure, a priori intuition in his philosophy which he borrowed from the Kantian tradition.