For hypertensive patients, a real-time human physiological signal monitoring system helps to track blood pressure status and provides valuable data to clinicians for early diagnosis and timely intervention. Optical fiber pulse sensing has superior conditions such as resistance to electromagnetic interference and richness of measured pulse characteristics. In this study, a monitoring system based on a single-point curved fiber pulse sensor (CFPS) was used to collect the pulse wave signal of a human radial artery. The features of the pulse wave signal were used to estimate the pulse wave transit time (PTT) and Blood Pressure—systolic blood pressure (SBP) and diastolic blood pressure (DBP)—based on support vector regression (SVR) optimized by a genetic algorithm (GA) (GA-SVR model). The results show that the root mean square error (RMSE) of SBP, DBP and PTT were 1.571 mmHg, 3.250 mmHg and 5.719 ms, respectively, and the results met the Advancement of Medical Instrumentation (AAMI) criteria. Therefore, a real-time pulse wave monitoring system based on a single-point CFPS can well predict human physiological signals such as PTT, SBP and DBP.