The effect of beam position error on the imaging quality of a Fourier telescope is analyzed in this paper. First, the origin of the transmitting beam position error and the error types are discussed. Second, a numerical analysis is performed. To focus on the transmitting beam position error, other noise sources exclusive of the reconstruction process are neglected. The Strehl ratio is set to be the objective function and the transfer function of the position error is constructed. Based on the numerical model, the features of Strehl ratio reduction caused by position error are deduced. Third, simulations are performed to study the position error effect on the imaging quality. A plot of the Strehl ratio versus the different levels of position errors is obtained and the simulation results validate the numerical model to a certain extent. According to the simulation results, a high value of the transmitting beam position error obviously degrades the imaging quality of the system; thus, it is essential to contain the position error within a relatively low level.