A cost-efficient dual-band transmission scheme based on return-to-zero (RTZ)-mode digital-to-analog converter (DAC) and sub-Nyquist sampling analog-to-digital converter (ADC) is proposed in this paper. The scheme can increase the data rate and meanwhile halve the required sampling rate of the DAC/ADC in optical intensity modulation direct detection (IMDD) transmission system. Based on this scheme, we experimentally demonstrate a dual-band discrete Fourier transformation spread (DFT-S) OFDM intensity modulation direct detection (IMDD) system. Although the sampling rate of the DAC and ADC used in the receiver is only 5-GSa/s and there is no mixer and oscillator at the transmitter and receiver side, 22-km standard single-mode fiber (SSMF) transmission with up to 26.33-Gb/s data rate is successfully realized. The experimental results show that in the system, the first sub-band transmission based on 128-QAM mapping can achieve a bit error rate (BER) below 3.8 × 10-3. The second sub-band transmission based on 32-QAM mapping can achieve a BER below 2.4 × 10-2. The spectral efficiency (SE) of the first sub-band signal is up to 6.14 bit/s/Hz and the SE of the second sub-band signal is up to 4.39 bit/s/Hz.