This letter offers a new frequency domain equalization (FDE) scheme that can work with a pseudo-random quantization (PRQ) scheme utilizing non-zero threshold quantization in one-bit uplink multi-user massive multiple-input multiple-output (MIMO) systems to mitigate quantization distortion and support high-order modulation schemes. The equalizer is based on Newton's method (NM) and applicable for orthogonal frequency division multiplexing (OFDM) transmission under frequency-selective fading by exploiting the properties of massive MIMO. We develop a low-complexity FDE scheme to obtain a quasi-Newton method. The proposed detector outperforms the benchmark detector with comparable complexity.