The nitrogen-vacancy (NV) centers ensemble has extensive application prospects in vector-magnetic-field measurement due to its accurate and fixed spatial orientations along the crystallographic axes of diamonds. However, to address signals of NV centers along all four axes, a large bias magnetic field sufficient to spectrally separate their resonances is typically inevitable, which may affect the magnetic substance under test and require multiple-frequency microwaves to interrogate signals of the four axes. Here, we demonstrate an NV-based simultaneous vector magnetometer that works at a bias field as low as just separating the resonant peaks of |ms=±1 states and utilizes a single-frequency microwave. By simultaneously detecting the fluorescence at specific optical polarization angles in three orthogonal directions and determining the transformation matrix in advance, all the Cartesian components of the magnetic field under test are distinguished. The experimentally achieved magnetic-field sensitivity is 63 nT/Hz, and the bias field is reduced to around 11 Gauss (still reducible by narrowing the linewidth) in ambient conditions. The proposed methods dramatically reduce the bias field for NV-based simultaneous vector magnetometers and potentially expand their applications in biological science, materials science, and industrial noninvasive detection.