Relativistic jets are observed throughout the Universe and strongly affect their surrounding environments on a range of physical scales, from Galactic binary systems(1) to galaxies and clusters of galaxies(2). All types of accreting black hole and neutron star have been observed to launch jets(3), with the exception of neutron stars with strong magnetic fields(4,5) (higher than 1012 gauss), leading to the conclusion that their magnetic field strength inhibits jet formation(6). However, radio emission recently detected from two such objects could have a jet origin, among other possible explanations(7,8), indicating that this long-standing idea might need to be reconsidered. But definitive observational evidence of such jets is still lacking. Here we report observations of an evolving jet launched by a strongly magnetized neutron star accreting above the theoretical maximum rate given by the Eddington limit. The radio luminosity of the jet is two orders of magnitude fainter than those seen in other neutron stars with similar X-ray luminosities(9), implying an important role for the properties of the neutron star in regulating jet power. Our result also shows that the strong magnetic fields of ultra-luminous X-ray pulsars do not prevent such sources from launching jets.