Accurate short-term passenger flow prediction in urban rail transit stations has great benefits for reasonably allocating resources, easing congestion, and reducing operational risks. However, compared with data-rich stations, the passenger flow prediction in newly-operated stations is limited by passenger flow data volume, which would reduce the prediction accuracy and increase the difficulty for station management and operation. Hence, how accurately predicting passenger flow in newly-operated stations with limited data is an urgent problem to be solved. Existing passenger flow prediction approaches generally depend on sufficient data, which might be unsuitable for newly-operated stations. Therefore, we propose a meta-learning method named Meta Long Short-Term Memory Network (Meta-LSTM) to predict the passenger flow in newly-operated stations. The Meta-LSTM is to construct a framework that increases the generalization ability of long short-term memory network (LSTM) to various passenger flow characteristics by learning passenger flow characteristics from multiple data-rich stations and then applying the learned parameter to data-scarce stations by parameter initialization. The Meta-LSTM is applied to the subway network of Nanning, Hangzhou, and Beijing, China. The experiments on three real-world subway networks demonstrate the effectiveness of our proposed Meta-LSTM over several competitive baseline models. Results also show that our proposed Meta-LSTM has a good generalization ability to various passenger flow characteristics, which can provide a reference for passenger flow prediction in the stations with limited data.