Geo-magnetically induced currents (GICs) have attracted more attention since many Ultra-High Voltage (UHV) transmission lines have been built, or are going to be built in the world. However, when calculating GICs based on the classical model, some input parameters, such as the earth conductivity and dc resistances of the grid, are uncertain or very hard to be determined in advance. Taking this into account, the uncertainty quantification (UQ) model of the geo-electric fields and GICs is proposed in this paper. The UQ of the maximums of the geo-electric fields and GICs during storms is carried out based on the polynomial chaos (PC) method. The results of the UHV grid, 1000 kV Sanhua Grid, were presented and compared to the Monte Carlo method. The total Sobol indices are calculated by using the PC expansion coefficients. The sensitivities of geo-electric fields and GICs to the input variables are analyzed based on the total Sobol indices. Results show that the GICs and geo-electric fields can be effectively simulated by the proposed model, which may offer a better understanding of the sensitivities to input uncertain variables and further give a reasonable evaluation of the geomagnetic threat to the grid.