Abstract: Based on the principles of diffraction enhanced imaging(DEI) and grating-based phase-contrast imaging,the reconstruction algorithms for differential phase-contrast CT(DPC-CT) are discussed,including the latest developments,the main ideas and their properties.These algorithms are combination between the physics principles of phase-contrast imaging and conventional CT reconstruction theories,which can reconstruct the distribution of refractive index decrement in the sample from differential projection data directly,showing the interior structure of the low-Z weakly absorbing materials.