The direct detection of gravitational waves has started a new era of gravitational wave astronomy. As an important method for studying the counterparts of gravitational waves, the observation and search of the multi-wavelength radiation of the electromagnetic counterpart of gravitational waves has become the research focus in the field of astronomy. With the advancement of gravitational wave detectors, the number of gravitational wave samples has dramatically increased and the detection of gravitational wave electromagnetic counterparts has become very promising. The Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) satellite is a full-sky monitoring telescope designed for detecting high-energy electromagnetic counterparts of gravitational wave events. The main reason for designing a scientific application system of GECAM satellites, which is proposed and designed with an emphasis on discovery, is to ensure the scientific operation of the payload of satellites and achieve the production, storage, processing, calibration, release, and analysis of scientific data. It is also designed to provide technical support and services to scientific users. Based on the exploration and research of the gravitational wave electromagnetic counterpart, this article introduces an innovative monitoring method design of the GECAM scientific application system for the gravitational electromagnetic counterpart, namely, the scheme design of the GECAM scientific application system. The design covers system architecture, interface control, main technical processes, functional composition, and software planning and design. The GECAM satellite is scheduled for launch by the end of 2020. By then, the scientific application system will be able to support the satellite’s in-orbit scientific operation and research.