The development of air traffic trajectory prediction models is a key objective of the next generation (NextGen) national air transportation system. Significant uncertainties associated with weather conditions exist in the current trajectory prediction methods and should be properly addressed. This paper proposes a novel Conditional Generative Adversarial Network (CGAN) approach for weather-related aircraft trajectory prediction problems. The problem is formulated as predicting the trajectory and conditioning on the last on-file flight plan and weather effects. The generator network includes two convolutional layers and two dense layers for weather feature extraction. Then the extracted features, concatenating with the conditional inputs are feed into a single layer long short-term network to output the generated trajectory. The discriminator network has a similar architecture but is trying to discriminate the inputs from the ground truth dataset and the generated trajectory. The experiment is conducted with the data obtained from Sherlock Data Warehouse (SDW). We are using the flight data from Indianapolis Air Route Traffic Control Center (ZID) and the EchoTop (ET) weather features within the sector airspace on June 24th, 2019. The experimental result shows the mean prediction has a better overall variance reduction compared to our previous work. The model is able to output confidence intervals (CI) of the prediction by sampling random noise as the inputs to the generator.