The diagnoses of laser-produced plasma electron density have important significance for inertial confinement fusion, plasma physics, high energy density physics and other relevant fields, especially for measuring electron density distribution information of medium and high-Z material plasma near the critical density surface. With 13.9 nm Ni-like Ag X-ray laser serving as a probe, using double frequency grating shearing interference technique, the electron density distribution of plasma produced by laser irradiating a gold planar target is measured. Clear interference fringe image is obtained. Preliminary deduction of the fringe shows that the maximum density measured is about 1.4 times the critical density. It is found that there are some discrepancies between experimental results and simulation results, which provides a useful reference to the further optimization of the simulation program. The experimental results fully demonstrate that the soft X-ray double frequency grating shearing interference technique is practical to diagnose near-critical-density plasma of medium and high-Z materials, which will have a good application value.