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Highly accurate trajectory prediction models can achieve route optimisation and save airspace resources, which is a crucial technology and research focus for the new generation of intelligent air traffic control. Aiming at the problems of inadequate extraction of trajectory features and difficulty in overcoming the short-term memory of time series in existing trajectory prediction, a trajectory prediction model based on a convolutional neural network-bidirectional long short-term memory (CNN-BiLSTM) network combined with dual attention and genetic algorithm (GA) optimisation is proposed. First, to autonomously mine the data association between input features and trajectory features as well as highlight the influence of important features, an attention mechanism was added to a conventional CNN architecture to develop a feature attention module. An attention mechanism was introduced at the output of the BiLSTM network to form a temporal attention module to enhance the influence of important historical information, and GA was used to optimise the hyperparameters of the model to achieve the best performance. Finally, a multifaceted comparison with other typical time-series prediction models based on real flight data verifies that the prediction model based on hyperparameter optimisation and a dual attention mechanism has significant advantages in terms of prediction accuracy and applicability.