X-ray phase-contrast imaging is one of the novel techniques,and has potential to enhance image quality and provide the details of inner structures nondestructively.In this work,we investigate quantitatively signal-to-noise ratio (SNR) of grating-based x-ray phase contrast imaging (GBPCI) system by employing angular signal radiography (ASR).Moreover,photon statistics and mechanical error that is a major source of noise are investigated in detail.Results show the dependence of SNR on the system parameters and the effects on the extracted absorption,refraction and scattering images.Our conclusions can be used to optimize the system design for upcoming practical applications in the areas such as material science and biomedical imaging.