The transmission error of a gear pair is one of the main excitations that cause the vibration and noise problems of gearboxes. The root causes of the transmission error include the gear manufacturing errors, the installing errors and the elastic deformation of meshing gear teeth. Although the transmission error have a significant influence on the dynamics of gear pairs, most of the previous studies just employ simplified mathematical functions to qualitatively represent its periodicity. Only recently, the experimental study was conducted to investigate the detailed properties of the transmission errors in quasi-static conditions, which requires strong expertise and costly precision equipment. Therefore, to give a quick evaluation of the properties of transmission error, this paper proposes a virtual model to numerically predict the transmission error of a spur gear pair in the static condition. The model is capable to simulate the transmission error that is caused by typical gear manufacturing and installing errors like the indexing errors and run-out errors. The simulated transmission errors agree with the experimental phenomenon observed in previous published works. The proposed virtual model has the potential to assist in the in-depth analysis and modeling of dynamic behavior of gear transmissions.