Covert communication aims to hide the very existence of wireless transmissions in order to guarantee a strong security in wireless networks. In this work, we examine the possibility and achievable performance of covert communication in one-way relay networks. Specifically, the relay is greedy and opportunistically transmits its own information to the destination covertly on top of forwarding the source's message, while the source tries to detect this covert transmission to discover the illegitimate usage of the resource (e.g., power, spectrum) allocated only for the purpose of forwarding source's information. We propose two strategies for the relay to transmit its covert information, namely fixed-rate and fixed-power transmission schemes, for which the source's detection limits are analysed in terms of the false alarm and miss detection rates and the achievable effective covert rates from the relay to destination are derived. Our examination determines the conditions under which the fixed-rate transmission scheme outperforms the fixed-power transmission scheme, and vice versa, which enables the relay to achieve the maximum effective covert rate. Our analysis indicates that the relay has to forward the source's message to shield its covert transmission and the effective covert rate increases with its forwarding ability (e.g., its maximum transmit power).