St. Anselm (c. 1033-1109) introduced an argument on the existence of God which is now known as the Ontological Argument, according to which God is defined as the most perfect being imaginable, or in the most famous formulation of the Argument, given by him, that being than which nothing greater can be thought. At the outset, this article is concerned wiht the very term "Ontological Argument" to specify why this is so denominated; the Argument is held to have been influenced by Kant's triadic division. Moreover, the criticisms made by Gaunilon and Aquinas on the Argument and some illuminating remarks related to it are discussed. In the meantime, some major objections - with respect to conceptual precision - raised by Moslem scholars against Anselm's Argument are put forward. The main point of the article concerned with the precise investigation into Anselm's Argument made by Moslem philosophers reveals the great capability of Islamic philosophy in various aspects.