The grinding process is very complex and relates many parameters to control the process. As this reason, a theoretical analysis and a quantitative estimation of the grinding process has not been well established. In this study, the in-process monitoring system was suggested by applying the neural network for monitoring and shooting the malfunction of cylindrical plunge grinding process. This system used the power signals from the electric power meter. This neural network was composed of processing elements [4-(5-5)-3] with 4 identified power parameters. Because sensitivity is blunted some minute vibration components, the simulation result of this system has appeared about 10% erroneous recognition in the uncertain pattern and the average success rate of the trouble recognition was about 90%. Consequently, the developed system, which applied to the power signals, can be recognize enough to monitor the grinding process as in-process.