A homogeneous Markov chain model is proposed to make delay analysis and prediction for near future train movements in a non-periodic single-track railway timetable setting. The prediction model constitutes two principal processes, namely sectional running and conflict resolution, which are represented by the stochastic recovery and deterioration matrices, respectively. The matrices are developed using a data-driven approach. Given the initial delay of a train at the beginning of the prediction horizon, its delay within the horizon can be estimated by vector and matrix operations, which are performed for individual processes separately or in combination of the processes. A baseline linear model has also been developed for comparison. The numerical tests conducted give consistent and stable predictions for train delays made by the Markov model. This is mainly because of that the Markov model can capture uncertainties deep in the horizon and respond to variations in train movements.