The use of low-resolution analog-to-digital converters (ADCs) (i.e., 1-3 bits) in a receiver effectively decreases power consumption and system costs, especially for millimeter-wave wireless systems. However, the orthogonality among subcarriers in the orthogonal frequency division multiplexing (OFDM) system cannot be maintained because of the severe nonlinearity of a low-resolution ADC. This paper proposes the optimal data detection algorithm for this quantized OFDM system. Simulation results demonstrate that the proposed algorithm, which entails acceptable performance loss compared to the infinite-precision case, significantly outperforms the conventional OFDM receiver in terms of symbol error rate.