Recently, WLANs using multiple frequency bands (e.g., 5 GHz, 2.4 GHz, and 920 MHz) have become popular as a means to increase spectral efficiency. However, during multi-hop transmissions in such multi-band WLANs, the relay node experiences a significant increase in delay and loss of data frames. This happens because of the difference of link rates between the receiving and sending sides of the relay node. In order to address this problem, we consider the channel conditions of each band on either side of the relay. Accordingly, the receiving and sending rates at the relay node are measured and calculated, respectively. Based on the measured receiving rate and calculated sending rate, we propose an algorithm for the relay node to determine the optimal coding rate and modulation method so as to dynamically control the best band and channel selection for the sending side. Simulation results demonstrate the effectiveness of our proposed algorithm in terms of improvement of delay and transmission failure probability.