Abstract: In this paper, the authors consider the $\omega$-type Calderón-Zygmund operator $T_{\omega}$ and the commutator $[b,T_{\omega}]$ generated by a symbol function $b$ on the Lorentz space $L^{p,r}(X)$ over the homogeneous space $(X,d,\mu)$. The boundedness and the compactness of the commutator $[b,T_{\omega}]$ on Lorentz space $L^{p,r}(X)$ are founded for any $p\in (1, \infty)$ and $r\in [1, \infty)$.

Key words: $\omega$-type Calderón-Zygmund operator, commutators, Lorentz space, homogeneous space