X-ray phase-contrast imaging based on grating interferometry is a technique with the potential to provide absorption, differential phase contrast, and dark-field signals simultaneously. The multi-line X-ray source used recently in grating interferometry has the advantage of high-energy X-rays for imaging of thick samples for most clinical and industrial investigations. However, it has a drawback of limited field of view (FOV), because of the axial extension of the X-ray emission area. In this paper, we analyze the effects of axial extension of the multi-line X-ray source on the FOV and its improvement in terms of Fresnel diffraction theory. Computer simulation results show that the FOV limitation can be overcome by use of an alternative X-ray tube with a specially designed multi-step anode. The FOV of this newly designed X-ray source can be approximately four times larger than that of the multi-line X-ray source in the same emission area. This might be beneficial for the applications of X-ray phase contrast imaging in materials science, biology, medicine, and industry.