  We study the entanglement entropy of theories that are derived from relevant
perturbation of given CFTs for regions with a singular boundary by using the
AdS/CFT correspondence. In the smooth case, it is well known that a relevant
deformation of the boundary theory by the relevant operator with scaling
dimension $\Delta=\frac{d+2}{2}$ generates a logarithmic universal term to the
entanglement entropy. As the smooth case, when the boundary CFT deformed by a
relevant operator, we find that the entanglement entropy of singular surface
also contains a new logarithmic term which is due to relevant perturbation of
the conformal field theory, and depends on the scaling dimension of relevant
operator. We also find for extended singular surfaces, $c_{n}\times R^{m}$, as
well as logarithmic term, the new universal double logarithmic terms may appear
depending on the scaling dimension of relevant operator and spacetime
dimensions. These new terms are due to relevant perturbation of the boundary
theory.
