  This paper is devoted to the construction of the Hamiltonian for
non-relativistic string in the Newton-Cartan background. We start with the
Hamiltonian for relativistic string in general background. Then we perform
limiting procedure on the metric that leads to Newton-Cartan background. We
determine constraint structure for non-relativistic string and show that these
constraints are the first class constraints. Then we determine corresponding
Lagrangian and discuss its properties.
