In this paper, we propose wav-U-Net to improve speech enhancement in heavy noisy environments, and it has implemented three principal techniques. First, as input data, we use 128 modified Mel-scale filter banks which can reduce computational burden instead of 512 frequency bins. Mel-scale aims to mimic the non-linear human ear perception of sound by being more discriminative at lower frequencies and less discriminative at higher frequencies. Therefore, Mel-scale is the suitable feature considering both performance and computing power because our proposed network focuses on speech signals. Second, we add a simple ResNet as pre-processing that helps our proposed network make estimated speech signals clear and suppress high-frequency noises. Finally, the proposed U-Net model shows significant performance regardless of the kinds of noise. Especially, despite using a single channel, we confirmed that it can well deal with non-stationary noises whose frequency properties are dynamically changed, and it is possible to estimate speech signals from noisy speech signals even in extremely noisy environments where noises are much lauder than speech (less than SNR 0dB). The performance on our proposed wav-U-Net was improved by about 200% on SDR and 460% on NSDR compared to the conventional Jansson's wav-U-Net. Also, it was confirmed that the processing time of out wav-U-Net with 128 modified Mel-scale filter banks was about 2.7 times faster than the common wav-U-Net with 512 frequency bins as input values.