In orthogonal frequency division multiple access - code division multiplexing (OFDMA-CDM), rate adaptation is known as one of the key techniques to improve the reliability of the transmission signal. However, since the one subchannel size in OFDMA-CDM depends on the spreading code length, the fading shift which the transmission signal receives per one subchannel might depend on the spreading code length. If the influence of the fading shift can be suppressed according to the multiplexing ratio, the effect of the rate adaptation can be improved. In addition, by allocating the subchannel with multiuser diversity in OFDMA, the effect of the rate adaptation can be more improved. We propose a subchannel allocation scheme based on the maximum, minimum and average signal to interference plus noise ratio (SINR) and orthogonal variable spreading factor (OVSF) code allocation to despread in narrowband according to the multiplexing ratio. We demonstrate that the proposed scheme can improve the bit error rate (BER) performance.