Grating-based X-ray phase-contrast imaging (GPCI) provide complementary attenuation, phase, and scattering contrasts simultaneously, especially useful for imaging samples comprising of mostly low atomic number elements (low-Z materials). These powerful imaging abilities have important applications in medical diagnostics and biological research. Critical optical components such as gratings in GPCI make GPCI more sensitive, at the cost of difficulties in the experimental operation. In this study, a new detector image correction method in GPCI is developed to simplify the data collection and image processing. Generally, both offset (dark-current) and gain corrections need to be performed for conventional image correction. Based on the principle of GPCI, here we analyze theoretically the influences of dark-current and inhomogeneity of the detector on the images of GPCI, and find that only the offset correction is necessary for the attenuation and scattering contrast images. Then, a simplified image correction method without gain correction is proposed for GPCI. The experiments performed on a prototype for non-interferometric grating-based X-ray phase-contrast imaging confirm the feasibility and validity of the proposed method. Compared with conventional image correction, the new image correction method can achieve the same performance only with offset correction. Therefore, the new method simplifies the experimental operation and facilitates the use of GPCI for radiographic applications in materials science, biomedical imaging, and industrial non-destructive inspection.