  In this paper, we investigate the entanglement entropy for the generalized
charged BTZ black hole through the $AdS_{3}/CFT_{2}$ correspondence. Using the
holographic description of the entanglement entropy for the strip-subsystem in
boundary $CFT_{2}$, we will find the first law-like relation between the
variation of holographic entanglement entropy and the variation of energy of
the subsystem in terms of the mass and the electric charge up to the second
order. We also obtain appropriate counterterms to renormalize the energy tensor
associated with the bulk on-shell actions.
