Sensing vector magnetic fields is critical to many applications in fundamental physics, bioimaging, and material science. Magnetic-field sensors exploiting nitrogen-vacancy (NV) centers are particularly compelling as they offer high sensitivity and spatial resolution even at nanoscale. Achieving vector magnetometry has, however, often required applying microwaves sequentially or simultaneously, limiting the sensors applications under cryogenic temperature. Here we propose and demonstrate a microwave-free vector magnetometer that simultaneously measures all Cartesian components of a magnetic field using NV ensembles in diamond. In particular, the present magnetometer leverages the level anticrossing in the triplet ground state at 102.4 mT, allowing the measurement of both longitudinal and transverse fields with a wide bandwidth from zero to megahertz range. Full vector sensing capability is proffered by modulating fields along the preferential NV axis and in the transverse plane and subsequent demodulation of the signal. This sensor exhibits a root mean square noise floor of about 300 pT/Hz^(1/2) in all directions. The present technique is broadly applicable to both ensemble sensors and potentially also single-NV sensors, extending the vector capability to nanoscale measurement under ambient temperatures.