A special differential interferometer consisting of two gratings was developed for diagnostics of plasma density. Compared with other differential interferometers, our system has an important advantage that the shear distance, shear direction, and fringe width can be adjusted independently, enabling easy control of the parameters. This feature allows precise tuning of the two probe beams in the interferometer for rigorous differential phase diagnosis and more accurate information of the plasma density can be obtained. The double-grating-based differential interferometer was tested for diagnostics of the laser-produced plasma which was generated by focusing a 1 TW/35 fs Ti:sapphire laser pulse in a gas jet with a 100 μm orifice diameter. It was confirmed that our differential interferometer can provide more reliable and accurate plasma density information, especially for plasmas with a high spatial gradient in density.