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Covert wireless communication aims to hide the very existence of wireless transmissions in order to guarantee a strong security in wireless networks. In this paper, we examine the possibility and achievable performance of covert communication in amplify-and-forward 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 and spectrum) allocated only for the purpose of forwarding the source's information. We propose two strategies for the relay to transmit its covert information, namely rate-control and power-control transmission schemes, for which the source's detection limits are analyzed in terms of detection error probability and the achievable effective covert rates from the relay to destination are derived. Our examination determines the conditions under which the rate-control transmission scheme outperforms the power-control 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 transmits power).