This paper presents a deep neural network (DNN)-based speech enhancement algorithm based on the soft audible noise masking for the single-channel wind noise reduction. To reduce the low-frequency residual noise, the psychoacoustic model is adopted to calculate the masking threshold from the estimated clean speech spectrum. The gain for noise suppression is obtained based on soft audible noise masking by comparing the estimated wind noise spectrum with the masking threshold. To deal with the abruptly time-varying noisy signals, two separate DNN models are utilized to estimate the spectra of clean speech and wind noise components. Experimental results on the subjective and objective quality tests show that the proposed algorithm achieves the better performance compared with the conventional DNN-based wind noise reduction method.