Due to the high orbital altitude, the large‐area antenna and solar array will be utilised in geosynchronous synthetic aperture radar (GEO SAR) to meet the requirement of high transmitting power. However, the large‐area antenna and solar array can easily cause antenna translation vibration (ATV) and further result in paired echo, which will seriously affect the GEO SAR image quality. Existing effect analyses of antenna vibration for low‐earth‐orbit SAR (LEO SAR) based on the linear trajectory and the corresponding second‐order Doppler spectrum cannot be applied in GEO SAR because of its extremely long synthetic aperture time (SAT), curved trajectory, and corresponding high‐order Doppler spectrum. To analyse the effects of ATV on GEO SAR image, the ideal echo signal model and the corresponding point spread function (PSF) of GEO SAR are first established and deducted, respectively. Then, the echo signal model and PSF affected by ATV are obtained. Based on the affected PSF, the effects of the ATV on GEO SAR image are analysed in detail, and the basis for subsequent ATV suppression is also obtained. Computer simulations validate the correctness of the analyses shown here.