Terahertz time-domain spectroscopy can extract the optical constants of materials in the terahertz region rapidly and accurately. However, the errors of various components in the control precision, response error, system noise, experiment operation and data processing will affect the accuracy of the extracted optical constants of materials. Based on the measurement principle of transmission terahertz time domain spectroscopy, the influence on the accuracy of the system delay-line position deviation on extracting the complex index of refraction of materials was analysed in this paper, and the error on propagation through the measurement process was modeled. Simulation was carried out to illustrate the relation between the error and the uncertainty in the extracted complex index of refraction of materials. The results showed that the uncertainty of complex index of refraction of the sample is influenced by the system delay-line position. The larger the system delay-line position deviation is, the greater the uncertainty of the extraction in the complex index of refraction of the sample will be. Meanwhile, compared to coefficient of light extinction, the system delay-line position deviation has greater influence on the uncertainty of refractive index of the sample. The model has some practical significance and theoretical reference value, which can analyze the influence of the system delay-line position deviation on extracting the optical constants of materials, and provide theoretical suggestions for the optimization of terahertz time-domain spectroscopy.