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Climate models help us simulate and predict how the Earth's climate is going to change in the future. Wind speed data is critical for developing and validating such models. However, in the real world, often owing to many factors such as station maintenance and sensor failures, a considerable amount of wind data goes missing. The Generative Adversarial Network (GAN) has been used to impute missing wind data, but the handling of unrealistic GAN output has remained largely unstudied. In this paper, we propose a novel hybrid approach that combines both the GAN and dual annealing algorithms to not only impute missing wind speed data but also counter unrealistic GAN outcomes. The hourly mean wind data has been collected from the National Centers for Environmental Information for four Indian stations, viz. Ahmedabad, Indore, Mangaluru and Mumbai. We compared the performance of the proposed approach with those of k-nn, soft imputation, and plain GAN-based approaches on mean, variance, standard deviation, kurtosis, skewness, and R-square. We found that our approach ranks number one based on the R-square value for all the considered stations. Our model consistently produces realistic results, unlike plain GAN. We observed that Mumbai has the lowest percentage of missing data (13.14%) and the highest R-square value (0.9999186451). However, Indore has the highest percentage of missing data (46.6463%) and the lowest R-square value (0.9046885604). [ABSTRACT FROM AUTHOR]