  We generalize recent analysis of the dynamics of point particle in
Horava-Lifshitz background to the case of string probe when we replace the
Hamiltonian constraint of the Polyakov string with the constraint that breaks
Lorentz invariance of target space-time. Then we find corresponding Lagrangian
and argue that the world-sheet theory is invariant under foliation preserving
diffeomorphism. Finally we discuss the Hamiltonian dynamics and show that this
is well defined on condition that the world-sheet lapse function obeys the
projectability condition.
