The purpose of this study is to present a new function point estimation approach for the Object-Oriented information systems. In order to fulfill this purpose, we first review the literature on Function Point Analysis of IFPUG, Unified Modeling Language, and Unified Process. Then, we derive a method and rules for estimating Function Points based on Use Cases and Class Diagrams. To analyze the appropriateness of the proposed approach, we conduct the empirical testing. 143 use cases are collected from production, marketing, distribution, sales, and other areas from the Object-Oriented systems development projects. We compare our new approach with the existing methods that are usually used for traditional systems development projects. The results show that our proposed approach is more appropriate for the Object-Oriented environment.