This paper proposes a high-sensitivity fiber magnetic field sensor based on a Mach-Zehnder interferometer and a photoelectric oscillator. According to the principle of the sensor based on the photoelectric oscillator, the relationship between the wavelength sensitivity of the designed Mach-Zehnder interferometer and the frequency sensitivity of the photoelectric oscillator is established, revealing that the frequency sensitivity of the photoelectric oscillator increases as the wavelength sensitivity increases. In this design, the Mach-Zehnder interferometer is constructed by splicing a tapered fiber between two single-mode fibers with an offset, which can split the light emitted by a broadband light source into sinusoidal-shaped waves. Experimental results show that within the magnetic field range of 1.6 mT to 12.8 mT, the frequency sensitivity of the sensor is 324 Hz/mT, with a corresponding measurement error within ±0.96 mT.