Following Jiang Guanghao and Xu Luoshan's concept of conjugative, dually conjugative, normal and dually normal relations on sets, %introduced in articles \cite{4}, \cite{5} and \cite{6}, the concept of quasi-regular relations is introduced. Characterizations of quasi-regular relations are obtained and it is shown when an anti-order relation is quasi-regular. Some nontrivial examples of quasi-regular relations are given. At the end we introduce dually quasi-regular relations and give a connection between these two types of relations.