In order to estimate the icing growth characteristics of stay cables in the ice prone area in winter, the grey correlation analysis method is used to analyze the correlation effects of inclination angle, temperature, humidity, wind speed, rainfall and air pressure on the icing thickness of stay cables, and the correlation of each influential factor is determined. Then, the genetic algorithm (GA) and the whale algorithm (WOA) are combined to select the optimal smoothing factor, and a WOA-GA Optimized Generalized Regression Neural Network (GRNN) method is proposed to predict the icing thickness of stay cables. Its characteristic is to take the mean square deviation of output value and actual value as fitness function, and to calculate the fitness value of each particle; introducing the crossover and mutation operator of GA algorithm into WOA algorithm; meanwhile, via weight update strategy, the capacity of global optimization is improved, to prevent the WOA algorithm falling into local optimal; finally, through iterative optimization, the smooth factor corresponding to the minimum fitness value was output, and the GRNN pre optimization model was built. The results show that the correlation of ambient temperature is the highest, followed by dip angle, precipitation, wind speed and relative humidity, and the correlation of atmospheric pressure is the lowest; compared with the traditional GRNN, WOA-GRNN and PSO-GA-GRNN models, the proposed GRNN model has high accuracy, with the average mean absolute percentage error of 3.58% and root mean square error of 0.58 mm; The sensitivity analysis method is used to evaluate the impact of the influential factors on the accuracy of the model. It is found that the temperature has the greatest influence on the model, followed by the cable inclination.