This article analyzes the criminalization provisions of the International Convention for the Suppression of the Financing of Terrorism, the backbone of the legal regime for the prevention of terrorist financing. It makes a detailed examination of the background of the Convention and the nature of the negotiation discussions that led to its adoption. The drafters of the Convention were faced with two problems: first, how to define terrorism, terrorist acts, and terrorist groups, the financing of which should be addressed, second, the precise scope of the offense, in particular, how to define the preparatory acts of financing as an independent offense. This article argues that the definition of the offense provided by the Convention is far too ambiguous, and its application at national levels can often lead to an unjustifiable and unfair criminal law.