The XRISM is the X-ray astronomical mission led by JAXA/NASA/ESA with international participation, plan to be launched in 2022 (Japanese fiscal year), to quickly recover the high-resolution X-ray spectroscopy of astrophysical objects using the micro-calorimeter array after the failure of Hitomi. To enhance the scientific outputs of the mission, the Science Operations Team (SOT) is structured independently from the instrument teams and the mission operation team (MOT). The responsibilities of the SOT are summarized into four categories: 1) Guest observer program and data distributions, 2) Distribution of the analyses software and calibration database, 3) Guest observer supporting activities, and 4) the performance verification and optimization (PVO) activities. Before constructing the Operations Concept of the XRISM mission, the lessons on the Science Operations learned from the past Japanese X-ray missions (ASCA, Suzaku, and Hitomi) are reviewed, and 16 kinds of lessons are identified by the above categories: lessons on the importance of avoiding nonpublic (“animal”) tools, coding quality of public tools both on the engineering viewpoint and the calibration accuracy, tight communications with instrument teams and operations team, well-defined task division between scientists and engineers etc. Among these lessons, a) importance of the early preparations of the operations from the ground stage, b) construction of the independent team for the Science Operations from the instrument developments, and c) operations with well-defined duties by appointed members are recognized as the key lessons for XRISM. Then, i) the task division between the Mission and Science Operations and ii) the subgroup structure within the XRISM team are defined in detail as the XRISM Operations Concept. Then, following the Operations Concept, the detail plan of the Science Operations is designed as follows. The Science Operations tasks are shared among Japan, US, and Europe operated by three centers, the Science Operations Center (SOC) at JAXA, the Science Data Center (SDC) at NASA, and European Space Astronomy Centre (ESAC) at ESA. The SOT is defined as a combination of the SOC and SDC; the SOC is designed to perform tasks close to the spacecraft operations, such as spacecraft planning of science targets, quick-look health checks, pre-pipeline data processing, etc., and the SDC covers the tasks on the data calibration processing (pipeline processing), maintenance of the analysis tools etc. The data-archive and users-support activities are planned to be covered both by the SOC and SDC. Finally, the details of the Science Operations tasks and the tools for the Science Operations are also described in this paper. This information would be helpful for a construction of Science Operations of future X-ray missions.