Deep Neural Networks (DNN) have achieved tremendous success in various software applications. However, in accompany with outstanding effectiveness, DNN-driven software systems also exhibit incorrect behaviors and result in some critical accidents and losses. The testing and optimization of DNN-driven software systems rely on a large number of labeled data that often require many human efforts, resulting in high test costs and low efficiency. While some coverage-based criteria have been proposed for analyzing the feedforward neural networks (FNN), few criteria are effective on the Recurrent Neural Network (RNN)-based systems due to the particularity of their structure. In this paper, we propose DeepState, a test suit selection technique towards the particular neural network structures of RNN for quantitative analysis.DeepStateselects data based on a stateful perspective of RNN, which identifies the possibly misclassified test by capturing the state changes of neurons in RNN models. We further design a test selection method to enable testers to obtain a test suite with strong fault detection and model improvement capability from a large dataset. To evaluateDeepState, we conduct an extensive empirical study on popular datasets and prevalent RNNmodels containing image and text processing tasks. The experimental results demonstrate thatDeepStateoutperforms existing coverage-based techniques in selecting tests regarding effectiveness and the inclusiveness of bug cases. Meanwhile, we observe that the selected data can improve the robustness of RNN models effectively.