Most prediction models of drug-target binding affinity (DTA) treated drugs and targets as sequences, and feature extraction networks could not sufficiently extract features. Inspired by DeepDTA and GraphDTA, we proposed an improved model named GLSTM-DTA for DTA prediction, which combined Graph Neural Network (GNN) and Long Short-Term Memory Network (LSTM). The feature extraction block consists of two parts: GNN block and LSTM block, which extract drug features and protein features respectively. The novelty of our work is using LSTM, instead of Convolutional neural network (CNN) to extract protein sequence features, which is facilitating to capture long-term dependencies in sequence. In addition, we also converted drugs into graph structures and use GNN for feature extraction. The improved model performs better than DeepDTA and GraphDTA. The comprehensive results prove the advantages of our model in accurately predicting the binding affinity of drug-targets.