The broad-band fiber-optic λ/4 waveplate is a special birefringent fiber with a slowly varying spin rate. When the spin rate gradually increases, it could transform the linearly polarized light into the circularly polarized light, covering a broad frequency range. Based on the loop model, the influence of the broad-band fiber-optic λ/4 waveplate on the scale factor stability of the all-fiber optic current sensor was analyzed. The eigen-modes of the fast-spun end and the coupling coefficient between the two orthogonal eigen-modes, along with the temperature characteristics, were measured using the trajectories on the Poincare sphere. Experimental results show that when the spin rate meets certain conditions, the influence of the broad-band fiber-optic λ/4 waveplate on the scale factor stability induced by the temperature variation is less than 0.2%, much weaker than that of the narrow-band fiber-optic λ/4 waveplate. The temperature stability of the all-fiber optic current sensor could be improved by using broad-band fiber-optic λ/4 waveplate.