We propose adaptive subcarrier selection (ACS) as an efficient technique of improving the error performance of grouped linear constellation precoding (GLCP) OFDM in the low-to-medium SNR range (0-20 dB). Recently, GLCP-OFDM has been proposed to achieve frequency diversity (multipath diversity) in OFDM overcoming the problem of channel nulls (deep fades in frequency-domain). In GLCP-OFDM, symbol precoding is performed on subgroups of OFDM subcarriers rather than on the total number of OFDM subcarriers which is large in practice. This reduces the receiver decoding complexity while maintaining the high SNR frequency diversity benefit - though the error performance in the low SNR regime is worse than a non-precoded system. In contrast, the proposed GLCP-ACS-OFDM improves the error performance in the low-to-medium SNR range without increasing the receiver complexity. Simulation results demonstrate the superior performance of GLCP-ACS-OFDM over GLCP-OFDM for a practical range of SNR as applicable to mobile wireless communications