Micro/nano spacecrafts need an attitude determination system performance in high accuracy, compact size, small mass and low power consumption. A novel inertial stellar compass (ISC) was designed to meet these requirements, which based on the gyroscope-free micro inertial measurement unit (GFMIMU) and integrated a star camera. The theory about how GFMIMU works to measure attitude angle was established. The state equation for ISC was modeled based on such theory, and the estimation equation was built up using measure information of the star camera. A Kalman filter approach was constructed to compensate the GFMIMU error in long-term working conditions, and the stability of the filter was proved using the observability analysis theory. A simulation of ISC was introduced finally, and the simulation results verify the proposed ISC can be used in micro/nano spacecrafts.