In recent years, the research for transmitter and receiver of terahertz is increasing with the development of terahertz devices. The working frequency and the bandwidth increase gradually, and the error caused by device non-ideality becomes an important factor affecting the performance of terahertz system. A Frequency Modulated Continuous Wave(FMCW) terahertz system with a two-stage mixing design is studied. This system has different sources of transmitter and receiver. The clock synchronization error, the frequency modulation nonlinear error, and the error from IQ unbalance are analyzed. The modeling of these three kinds of errors provides a theoretical basis for error elimination and compensation in the future.