  PSR J1357$-$6429 is a young radio pulsar that was detected in X-rays and
$\gamma$-rays. We present the high spatial resolution near-infrared imaging of
the pulsar field in $J$, $H$ and $K_s$ bands obtained with the VLT/NaCo using
the Adaptive Optic system. We found a faint source at the most precise pulsar
radio position which we propose as the pulsar near-infrared counterpart
candidate. It is confidently detected in the $J$ and $K_s$ bands, with $J$ =
23.51$\pm$0.24 and $K_s$ = 21.82$\pm$0.25. There is a hint of the source in the
$H$ band with an upper limit $H$ $>$ 22.8. The dereddened source fluxes are
compatible with the extrapolation of the pulsar X-ray spectrum towards the
near-infrared. If the candidate is the true counterpart, by this property PSR
J1357$-$6429 would be similar to the nearby middle-age pulsar PSR B0656+14. In
this case, both pulsars demonstrate an unusually high near-infrared efficiency
relative to the X-ray efficiency as compared to other pulsars detected in both
ranges.
