Full Function Point measurement method (COSMIC-FFP) is too abstract and difficult to be applied to object-oriented software. By analyzing the notional relationship between main components of UML and main elements of COSMIC-FFP, we establish 22 measurement mapping rules, propose UML-Based COSMIC-FFP method and list the measurement process and measurement steps. An example is given and the results show that this method can measure the functional size of object-oriented software objectively and effectively.