  On the basis of horizon thermodynamics, we study the thermodynamic stability
and $P-V$ criticality of topological black holes constructed in
Ho\v{r}ava-Lifshitz (HL) gravity without the detailed-balance condition (with
general $\epsilon$). In the framework of horizon thermodynamics, we do not need
the concrete black hole solution (the metric function) and the concrete matter
fields. It is shown that the HL black hole for $k=0$ is always
thermodynamically stable. For $k=1$, the thermodynamic behaviors and $P-V$
criticality of the HL black hole are similar to those of RN-AdS black hole for
some $\epsilon$. For $k=-1$, the temperature is classified into six types by
their different features. Among them, we mainly focus on the type with triply
degenerate thermodynamic state. It is also shown that there is a "thermodynamic
singularity" for the $k=-1$ HL black hole, where the temperature and Gibbs free
energy both diverge apart from a special pressure $P_s$.
