The shock wave driven by laser is an important tool for investigating equation of state and can provide the state of compressed matter. The X-ray source, generated by the short-pulse intense laser interaction with the solid target, has the properties of short pulse, small spot, high yield and tunable energy. Therefore the X-ray source is the first chosen as a backlighter for the diagnosis of dynamic process. The model of the X-ray radiography is established by Monte Carlo code Geant4. The density distribution in an object is obtained by hydrodynamic code Multi-1D and the laser parameters are obtained by the XGIII laser facility. Under the condition of one-dimensional density the object in the shape of rectangular solid, three evaluation criterions, root mean square, peak value and ratio of rise gradient, are defined for evaluating density results. The signal-to-noise, spatial resolution, and contrast of radiography results have been optimized. First, the signal-to-noise has been optimized and the optimization magnification is 5.6 with the photon yield 1012. Second, the spatial resolution according to different spot X-ray source has been simulated by designing resolution plate radiography. Third, in the condition of same magnification, the influence of source yield on radiography result has been analyzed. Fourth, the radiography results of different X-ray energy have been simulated. The optimization energy for radiography requests that the penetrability ratio is greater than 1.5 and the photon count in pixel after penetrating the compressed matter is greater than 3000. And the optimum criteria make sure that the radiography images simultaneously have high contrast and high signal-to-noise. The radiography of one-dimensional density object in the shape of cylinder has been simulated. The Abel inversion algorithm is established based on Radon inversion. The inversion result accords well with the designed density distribution in simulation at the request of the radius of X-ray source less than 5 m. The inversion result basically accords with the designed density distribution in simulation at the request of the radius of X-ray source less than 15 m. This work will contribute to the measurement experiments on the compressed matter achieved by laser-driven-shock and provide the reference for the optimization of radiography based on X-ray.