Let $T \in B({\cal H})$ be a bounded linear operator on a complex Hilbert space ${\cal H}$. $T$ is said to be log-hyponormal if $T$ is invertible 

and log$(TT^{*}) \ \le \ $log$(T^{*}T)$. In this paper we show that log-hyponormal operators have several spectral properties similar to $p$-hyponormal operators.