We propose a three-axis closed-loop optically pumped magnetometer with high sensitivity. The closed-loop magnetometer has a three-axis sensitivity of approximately 30 fT/Hz1/2 using two orthogonal laser beams for pumping and probing the alkali metal atoms. In the closed-loop mode, the dynamic range is improved from ±5 nT to ±150 nT. The bandwidth is increased from about 100 Hz to over 2 kHz with 10 kHz modulation fields in x- and y-axes and another 6 kHz modulation field along the z-axis. Compared with single-axis or dual-axis magnetometers, the proposed magnetometer not only provides the direction and magnitude of the magnetic field but also has high robustness in a challenging environment. The magnetometer has applications in biomagnetic measurements, magnetic resonance imaging, and fundamental physics.