In the hard X rays domain, the phase shift of the wave passing through the soft materials like tissues is typically three orders of magnitude larger than the absorption. Therefore the phase-sensitive X-ray imaging methods can obtain substantially increased contrast over conventional absorption-based imaging. In this paper, we present a detector system design for the computed tomography(CT) prototype which based on the grating-based phase contrast imaging(GBPCI) method. This system consists of 43 Hamamatsu silicon photodiode S12058(X) modules including 16512 pixels. Each module can provide 384(16*24) pixels, which the minimum pixel size is 0.75mm*1mm. The front-end readout electronics(FEE) of each module complete the analog-to-digital conversion, the digital processing, and the data transmission. All digitized data from 43 detector module are transmitted to the control system through the data collection boards. The test result shows that the efficient resolution of the detector system is up to 14.6bit. For all pixels, the integral nonlinearity is no more than 0.1%.