In this letter, the effect of a propagation delay resulting from the use of an OFDM system with a transparent mobile multi-hop relay (MMR) is initially analyzed. Then, a least square (LS) channel estimation technique for the OFDM system with throughput enhancement (TE) MMR or cooperative MMR is proposed. It is demonstrated by computer simulation that the proposed LS channel estimation technique for OFDM systems with transparent MMR is superior to the conventional technique in terms of mean square error (MSE) and bit error rate (BER).