PSR J1357 - 6429 is a Vela-like radio pulsar that has been recently detected with Chandra and Fermi , which , like Vela , powers a compact X-ray pulsar wind nebula and X-ray-radio plerion associated with an extended TeV source . We present our deep optical observations with the Very Large Telescope to search for an optical counterpart of the pulsar and its nebula . We detected a point-like source in V , R , and I bands whose position is in agreement with the X-ray position of the pulsar , and whose colours are distinct from those of ordinary stars . The tentative optical luminosity and efficiency of the source are similar to those of the Vela pulsar , which also supports the optical identification . However , the source spectrum is unusually steep , with a spectral index of about 5 , which is not typical of optical pulsars . The source offset from the radio position of PSR J1357 - 6429 , which is in line with the corresponding offset of the X-ray position , implies the pulsar transverse velocity of 1600–2000 km s ^ { -1 } at the distance of 2–2.5 kpc , making it the fastest moving pulsar known .