In the fiber optical synthetic aperture (FOSA) system, the diffraction of the Gaussian beam limited by the aperture in exit pupil plane of fiber collimator is studied theoretically, and the axial and transverse irradiance distributions are obtained. The point spread function (PSF) and modulation transfer function (MTF) of the truncated Gaussian beam array are computed numerically with different truncation factors. The results show that the diffraction of the truncated Gaussian beam array agrees with the uniform-beam Rayleigh diffraction when the truncation factor is less than 0.5, but little power is transmitted. The PSF and MTF are degraded, but more power can be contained when the truncation factor is larger. The selection of the truncation factor is a trade-off between the loss of transmission and the qualities of PSF and MTF in practical application.