The High Level Architecture (HLA) is the IEEE 1516 standard for interoperation between heterogeneous simulators which are developed with different languages and platforms. Run-Time Infrastructure (RTI) is a software which implements the HLA Interface Specification. With the development of time management service of RTI, it is necessary to consider an efficient design approach and an algorithm of Greatest Available Logical Time (GALT) computation. However, many time management services of existing RTIs have difficulty in modification and extension. Although some RTIs avoid this difficulty through modular design, they comply with not IEEE 1516 HLA/RTI but HLA 1.3. In addition, a lot of RTIs made use of well-known Matterns algorithm for GALT computation. However, Matterns algorithm has a few limitations for applying to IEEE 1516 HLA/RTI.This paper proposes a modular design and an implementation of time management service for IEEE 1516 HLA/RTI. We divided th time management service module into two sub-modules: a TIME module and a GALT module and used Matterns algorithm improved for IEEE 1516 HLA/RTI. The paper also contains several experimental results in order to evaluate our time management service module.