In recent years, graph-cuts has became increasingly useful methods for image processing problems such as the image denoising, the image segmentation, the stereo matching and so on. In graph-cuts, a given image is replaced by a grid graph with defined edge weights according to each problem, and the image is processed by using a minimum cut of the graph. Therefore, the most part of the graph-cuts algorithm is based on the typical minimum cut algorithm. However, graph-cuts still has two issues of processing time and accuracy of output images because of the conventional minimum cut algorithm. Moreover, the relation between the high-speed processing and the improvement of accuracy is basically a trade-off relation. In this research, we propose a new image denoising method using multiple-minimum cuts based on the maximum-flow neural network (MF-NN) which is our proposed minimum cut algorithm based on the nonlinear resistive circuit analysis. The MF-NN has two unique features not shared by the conventional minimum cut algorithm. One is that multiple-minimum cuts can be obtained simultaneously, and the other is to be suitable for hardware implementation. By using the MF-NN's features, the we find novel solutions for two issues of the conventional graph-cuts.