This paper proposes the Doppler frequency tracking system by the optimum synchronization technique which compensates the frequency shifts caused by satellite movement in a coherent digital satellite communication system. A Doppler frequency shift caused by satellite movements and the design theories of the optimum synchronization system are mathematically described. Based on this theory, a Doppler frequency tracking system is implemented via digital signal processing techniques utilizing a DSP chip, RAMs, PROMs, and a 80286 microprocessor. The performance of the designed system was evaluated through the experiments with the INTELSATVA satellite.