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• A large bandwidth optical fiber magnetic field sensor based on Sagnac interferometer for weak alternating magnetic fields measurement is proposed. • The sensing mechanism of this magnetic field sensor under an alternating magnetic field is theoretically derived and simulated. • The experimental system is built to verify the simulation results, and the magnetic field sensitivity is optimized by increasing the length of the delayed fiber ring. • The magnetic field sensor performances, such as frequency response, linear range, and noise, are analyzed theoretically and demonstrated experimentally. In this paper, a fiber magnetic field sensor is proposed based on Terfenol-D and Sagnac interferometer. The mechanism of the sensor is deduced theoretically. As the frequency of the magnetic field increases, on the one hand, the sensitivity is enhanced because the response to the high-frequency non-reciprocal phase differences is intensified in the Sagnac interferometer. On the other hand, the sensitivity is suppressed by the eddy current effect. Then it exhibits significant linear response to alternating magnetic field in a certain frequency range. The sensor performances, such as frequency response, linear range, and noise, are analyzed theoretically and demonstrated experimentally. Experimental results show that the sensor has a 3 dB bandwidth from 100 Hz to 2500 Hz, and the excellent linearity and reversibility from 0 to 274.05 μT (rms). The high sensitivity of 1.34 mV/μT (rms) and minimum detectable magnetic field of 25 nT/√Hz (rms) are achieved at 500 Hz. The sensor with large bandwidth and wide measuring range is suitable for detecting weak alternating magnetic field. [ABSTRACT FROM AUTHOR]