A fiber Bragg grating (FBG) pulse and systolic blood pressure (SBP) measurement system based on the edge-filtering method is proposed. The edge filter is the Mach-Zehnder interferometer (MZI) fabricated by two fiber couplers with a linear slope of 52.45 dBm/nm. The developed system consists of a broadband light source, an edge filter, fiber Bragg gratings (FBGs), a coarse wavelength-division multiplexer (CWDM), and signal-processing circuits based on a field-programmable gate array (FPGA). It can simultaneously measure pulse pulsations of the radial artery in the wrist at three positions: Cun, Guan and Chi. The SBP can be calculated based on the pulse transit time (PTT) principle. The measurement results compared to a standard blood pressure monitor showed the mean absolute error (MAE) and standard deviation (STD) of the SBP were 0.93 ± 3.13 mmHg. The system meets the requirements of the Association for the Advancement of Medical Instrumentation (AAMI) equipment standards. The proposed system can achieve continuous real-time measurement of pulse and SBP and has the advantages of fast detection speed, stable performance, and no compression sensation for subjects. The system has important application value in the fields of human health monitoring and medical device development.