  We construct a Josephson junction in non-relativistic case with a Lifshitz
geometry as the dual gravity. We investigate the effect of the Lifshitz scaling
in comparison with its relativistic counterpart. The standard sinusoidal
relation between the current and the phase difference is found for various
Lifshitz scalings characterised by the dynamical critical exponent. We also
find the exponential decreasing relation between the condensate of the scalar
operator within the barrier at zero current and the width of the weak link, as
well as the relation between the critical current and the width. Nevertheless,
the coherence lengths obtained from two exponential decreasing relations
generically have discrepancies for non-relativistic dual.
