The dispersion properties of linear birefringence and its effect upon the sensitivity of a bulk-glass optical current sensor are theoretically analyzed taking the Jones′ Matrix as a mathematical tool and simulated with a computer. The peak wavelength of the optical source used in an optical current sensing system will be changed by the fluctuations of the driving current or its ambient temperature. This will result in the fluctuation of the sensitivity of the system because of the dispersion of the linear birefringence existing inside the sensing head. The investigation results show that the dispersion will affect the scale factor of the system. But the effect is so small that can be omitted. These results might be useful for the researchers and designers working in the optical current sensing techniques area.