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Anesthesia induction is associated with frequent blood pressure fluctuation such as hypotension and hypertension. If it is possible to precisely predict blood pressure a few minutes ahead, anesthesiologists can proactively give anesthetic management before patients develop hemodynamic problem. The objective of this study is to develop a real-time model for predicting 3-min-ahead blood pressure from the start of anesthesia induction to surgical incision. We used only vital signs and anesthesia-related data obtained during anesthesia-induction phase and designed a bidirectional recurrent neural network followed by fully connected layers. We conducted experiments on our collected data of 102 patients, and obtained mean absolute errors between 8.2 mmHg and 11.1 mmHg and standard deviation between 8.7 mmHg and 12.7 mmHg. The average elapsed time for prediction of a batch of 100 unseen data was about 26.56 milliseconds. We believe that this study shows feasibility of real-time prediction of future blood pressures, and the performance will be improved by collecting more data and finding better model structures.