Newton’s gravitational constant G is the least known fundamental constant of nature. Since Cavendish made the first measurement of G with a torsion balance over two hundred years ago, the best results of G have been obtained by using torsion balances. However, the uncorrected anelasticity of torsion fibers makes the results questionable. We present a new method of G measurement by using a superconducting gravity gradiometer constructed with levitated test masses, which is free from the irregularities of mechanical suspension. The superconducting gravity gradiometer is rotated to generate a centrifugal acceleration that nulls the gravity field of the source mass, forming an artificial planetary system. This experiment has a potential accuracy of G better than 10 ppm.