In order to improve the accuracy of speech spoofing detection， a speech spoofing detection method based on LSTM-GRU network is proposed. LSTM-GRU network is a hybrid network combining long short-term memory（LSTM） layer， gated recurrent unit （GRU） layer， dropout layer， batch normalization layer and dense layer in series. LSTM layer can solve the problem of longtime dependence in speech sequence， while GRU layer can reduce the number of model parameters. The experiment is conducted on the ASVspoof2019 LA dataset， and the 20-dimensional Mel-frequency cepstral coefficient features are extracted for model training. In the test stage， the trained LSTM-GRU model is used for deception detection of the speech in the test set. By comparing with separate GRU and LSTM networks， the results show that： LSTM-GRU network achieves the highest correct recognition rate among the three network models； the equal error rate is 27.07% lower than the baseline system provided by the ASVspoof2019 challenge； the average accuracy of speech detection for logical access attack is 98.04%； LSTM-GRU network has the advantages of short training time， over-fitting prevention and high stability. It is proved that the proposed method can be effectively applied to speech logical access attack detection task.