  Some ones have showed the first-order phase transition of the Horava-Lifshitz
(HL) AdS black holes has unique characters from other AdS black holes. While
the coexistence zone of the first-order phase transition was not exhibited. As
well known the coexistence curve of a black hole carries a lot of information
about black hole, which provides a powerful diagnostic of the thermodynamic
properties on black hole. We study the first-order phase transition coexistence
curves of the HL AdS black holes by the Maxwell's equal-area law, and give the
boundary of two-phase coexistence zone. It is very interesting that the
first-order phase transition point is determined by the pressure F on the
surface of the HL AdS black hole's horizon, instead of only the pressure P (or
the temperature T). This unique property distinguishes the HL AdS black hole
from the other AdS black hole systems. Furthermore, this black hole system have
the critical curves, and on which every point stands for a critical point.
