We have been studying the use of multiple channel electroencephalogram (EEG) data to infer a human's thinking state. As a result, we have confirmed off-line thinking state estimation to be effective, in experimental studies on simulator training during malfunctions and mathematics problem solving. In this research, we developed a real-time system that monitors a human's thinking state on the basis of off-line results. First, an artificial neural network (ANN) model and a linear regression model were compared to determine which was more appropriate for real-time use. The ANN model was adopted because of its ease of handling and higher accuracy in thinking state estimation. Then, a prototype real-time thinking state monitoring (RTSM) system with the ANN model was developed and its effectiveness was evaluated experimentally via mathematics problem solving. Finally, we discuss a conception of plant operations with RTSM.