Grating based X-ray imaging technology is a coherent imaging technique that bears tremendous potential in three-dimensional tomographic imaging of weak absorption contrast specimens. Three kinds of contrast information including absorption, phase and scattering can be retrieved separately based on a single set of raw projections. However, the grating based X-ray imaging with the conventional phase-retrieval method using the conventional phase-stepping approach and filtered back projection (FBP) reconstruction algorithm require large amounts of raw data, so that long exposure time and large amounts of radiation dose is accepted by the sample. According to the traditional grating based X-ray imaging system, we propose a low dose, fast, multi-contrast CT reconstruction approach based on the iterative reconstruction algorithm that optimizes dose efficiency but does not share the main limitations of other reported methods. Prior to reconstruction, firstly, the projections are acquired with the phase stepping approach and multi-contrast projections are retrieved from the raw data by conventional retrieval algorithm. Then the rotational variable differential phase projections are converted to rotational invariable projections by means of decomposing the differential phase projections into the rotational invariable projections in two mutually perpendicular derivative directions via the transformation of coordinates. Finally, the absorption, phase and scattering information are reconstructed with the iterative reconstruction algorithm and the phase is retrieved based on the fast Fourier transform (FFT). We validated and assessed the phase reconstruction approach with a numerical simulation on a phase Shepp-Logan phantom. The experiment was performed at the X-ray imaging and biomedical application beam line (BL-13W) in the Shanghai Synchrotron Radiation Facility (SSRF) where 20 keV X-ray from a Si(111) monochromator is emitted. The X-ray interferometer was positioned at 34 m from the Wiggler source. The images were recorded with a scintillator/lens-coupled CCD camera with 2048 pixel2048 pixel resolution and an effective pixel size of 9 m. The numerical tests and the experimental results demonstrate that, for the small radiation dose deposited in the sample, the iterative reconstruction algorithm provides phase reconstructions of better quality and higher signal to noise ratio than the conventional FBP reconstruction algorithm, and also provides the multi-contrast 3D images, including absorption image, phase image and scattering image. This development is of particular interest for applications where the samples need inspecting under low dose and high speed conditions, and will play an important role in the nondestructive and quantitative imaging in the industry, biomedical and medical diagnosis fields.