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As the density of railway operations increases annually, train delays typically result in a greater degree of economic loss. If we can accurately assess the current evolution of delayed trains, railway authorities will be able to make timely decisions and reduce travel anxiety among passengers. In this paper, a deep learning model integrating wavelet transform (WT), fully connected neural network (FCNN), and long short-term memory (LSTM) network is proposed to address the short-term delay prediction problem for trains. Its predictive performance is enhanced by introducing two front train selection schemes, two methods for converting train operating time features into time-series data, and five commonly used wavelet functions. For validation purposes, the model is tested using real-world operational data from two distinct high-speed railway lines in China, and common machine learning algorithms are compared, including random forest (RF), gradient boosting regression tree (GBRT), XGBoosting (XGB), and support vector regression (SVR). The final experimental results demonstrate that our proposed model outperforms the benchmark models and can be effectively applied to practical prediction problems. • We investigate the spatio-temporal effects of delay propagation, categorizing delay data attributes into front trains and target trains. Two feature selection schemes are proposed to assess the impact of front train features on prediction performance. • Wavelet Transform (WT) is employed for the first time in train delay prediction to eliminate random interference. The model's prediction performance is enhanced through denoising and expanding feature dimensionality. • Real data from two Chinese high-speed railways validate the model's accuracy, providing practical guidance for its application. [ABSTRACT FROM AUTHOR]