In this paper, we propose a sub-Nyquist sampling (SNS) orthogonal frequency-division multiplexing (OFDM) radar system capable of reducing the analog-to-digital converter (ADC) sampling rate in OFDM radar without any additional manipulations of its hardware and waveform. To this end, the proposed system utilizes the ADC sampling rate of B/L to sample the received baseband signal with a bandwidth of B, where L is a positive proper divisor of the number of subcarriers. This divides the baseband signal into L sub-bands, folding into a sub-Nyquist frequency band due to aliasing. By leveraging known modulation symbols of the transmitted signal, the folded signal can be unfolded to the full-band signal. This allows an estimation of target ranges with the range resolution of the full signal bandwidth B without the degradation of the maximum unambiguous range. During the signal-unfolding process, the signals from other sub-bands remain as symbol-mismatch noise (SMN), which significantly degrades the signal-to-noise ratio (SNR) of the detected targets. It also causes weaker targets to be submerged under the noise in range profiles. To resolve this, a symbol-mismatch noise cancellation (SMNC) technique is also proposed, which reconstructs the interfering signals from the other sub-bands using the detected targets and subtracts them from the unfolded signal. As a result, the proposed sub-Nyquist sampling OFDM radar and corresponding signal processing technique enable a reduction in the ADC sampling rate by the ratio of L while incurring only a 10 log10 L increase in the noise due to noise folding. This is validated through simulations and measurements with various sub-sampling ratios.