A self-driven hybrid atomic spin oscillator is demonstrated in theory and experiment with a vapor Rb-Xe dual-spin system. The raw signal of Rb spin oscillation is amplified, phase-shifted, and sent back to drive the Xe spins coherently. By fine-tuning the driving-field strength and phase, a self-sustaining spin-oscillation signal with zero frequency shift is obtained. The effective coherence time is infinitely prolonged beyond the intrinsic coherence time of Xe spins, forming a hybrid atomic spin oscillator. Spectral analysis indicates that a frequency resolution of 13.1 nHz is achieved, increasing the detection sensitivity for a magnetic field. Allan-deviation analysis shows that the spin oscillator can operate in continuous-wave mode like a spin maser. The prototype spin oscillator can be easily incorporated into other hybrid spin systems and can increase the detection sensitivity of alkali-metal–noble-gas comagnetometers.