XRISM is an X-ray astronomical mission led by the Japan Aerospace Exploration Agency (JAXA) and National Aeronautics and Space Administration (NASA), with collaboration from the European Space Agency (ESA) and other international participants, that is planned for launch in 2022 (Japanese fiscal year), to quickly restore high-resolution X-ray spectroscopy of astrophysical objects using the micro-calorimeter array after the loss of Hitomi satellite. In order to enhance the scientific outputs of the mission, the Science Operations Team (SOT) is structured independently from the instrument teams and the Mission Operations Team (MOT). The responsibilities of the SOT are divided into four categories: 1) guest observer program and data distributions, 2) distribution of analysis software and the calibration database, 3) guest observer support activities, and 4) performance verification and optimization activities. Before constructing the operations concept of the XRISM mission, lessons on the science operations learned from past Japanese X-ray missions (ASCA, Suzaku, and Hitomi) are reviewed, and 15 kinds of lessons are identified by categories, such as lessons on the importance of avoiding nonpublic ("animal") tools, coding quality of public tools in terms of both the engineering viewpoint and calibration accuracy, tight communications with instrument teams and operations teams, well-defined task division between scientists and engineers, etc. Among these lessons, a) the importance of early preparation of the operations from the ground stage, b) construction of an independent team for science operations separate from the instrument development, and c) operations with well-defined duties by appointed members are recognized as key lessons for XRISM. Based on this, 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. Based on this operations concept, the detailed plan of the science operations is designed as follows. The science operations tasks are shared among Japan, the US, and Europe and are performed by three centers: the Science Operations Center (SOC) at JAXA, the Science Data Center (SDC) at NASA, and European Space Astronomy Centre (ESAC) at the 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 tasks regarding data calibration processing (pipeline processing), maintenance of analysis tools, etc. The data-archive and user-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 science operations are defined and prepared before launch. This information is expected to be helpful for the construction of science operations of future X-ray missions.