We propose a new time-division half-duplex estimate-and-forward (EF) relaying strategy suitable for a relay with mobility. We reconfigure EF relaying to guarantee a strong relay-destination link which is required to achieve a high rate using EF relaying. Based on the reconfigured model, we optimize the relaying strategy to attain a high rate irrespective of the relay position with preserving the total transmit bandwidth and energy. The proposed relaying strategy achieves high communication reliability for any relay position, which differs from conventional EF and decode-and-forward (DF) relaying schemes.