A fiber-optic vector magnetic field sensor based on a large-core-offset Mach-Zehnder interferometer (MZI) infiltrated by magnetic fluid (MF) is proposed and demonstrated in this paper. By large-core-offset fusion splicing of a short single-mode fiber (SMF) between a lead-in SMF and a coupling multi-mode fiber, the MZI with a sub-millimeter length is formed, which is then sealed in an MF-infiltrated glass capillary. Through the MF's refractive index modulation by external magnetic field, the phase of the light passing through the MZI is altered. As a result, the transmission spectrum can be monitored for the magnetic field measurement. Furthermore, from the axial-asymmetry of the large-core-offset MZI structure, the proposed sensor possesses vectorial magnetic-field-sensing ability. Experiments show that the MF-infiltrated large-core-offset MZI vector magnetic-field sensor can achieve a high wavelength sensitivity of 96.68 pm/Oe in a magnetic field range of 50-130 Oe.