Geomagnetically Induced Current (GIC) can cause DC bias of the transformer. The derivative effect of DC bias may threaten the safety of power equipment and power grid. In view of the fact that many input parameters are uncertain variables in GIC calculations, it is necessary to study the uncertainty of GIC and the sensitivity of GIC to input variables. In this paper, based on polynomial chaos expansion (PCE) and hyperbolic scheme for truncating the polynomial chaos expansion, a GIC uncertainty quantization method is proposed. Using the constructed polynomial chaos expansion, the sensitivity index of GIC to input parameters is derived. For the planned Xinjiang power grid, the proposed method is used to measure the uncertainty of GIC, and the statistics of mean and variance of GIC are obtained. The Sobol sensitivity index is calculated according to the chaotic polynomial coefficient, and the sensitivity of GIC to input parameters such as electric field amplitude and grid DC resistance is obtained. Compared with the Monte Carlo method (MC), this method is not only precise, but also greatly improves the computational efficiency.