Using physiological signals acquisition from wearable devices makes biometric identification more convenient and secure. Yet most of existing studies focus on Physiological signal-based biometric technology in a verification application rather than an identification application. Actually, identification application is a more general senior and there is an inevitable problem in discovering and identifying a new user. Existing approaches can only identify trained users and fail to join a new user into model conveniently, which limits identification application in human-computer interaction. In this work, we propose a physiological signal-based method for identifying both older users and new users. A deep network combining Transform and LSTM is introduced to extract user-specific features. Then, one-vs-all classifier is used to identify old users and discover a new user, and the classifier is updated to identify the new user without retraining whole model. Based on electrocardiogram (ECG) and photoplethysmography (PPG) signals in BIDMC dataset, our method achieved an accuracy of 99.52% and 99.30% for old users, as well as 93.18% and 91.23% for a new user. Extensive experiments demonstrate the performance in identifying old users and the effectiveness in discovering and identifying a new user via physiological signals.