Text tables play an important role in editable re-flowable documents. Analysis of the table logical structure can facilitate the standardization review, automatic processing and intelligent information extraction from the tables. However, the table logical structure is not stored in general re-flowable documents. In view of the complex format of the re-flowable documents, it is still challenging to analyze the table logical structure. To enable the computer to automatically interpret the table logical structure, a method for recognizing the table logical structure based on neural network is proposed. This method firstly establishes a fully connected neural network model to identify cell types, then builds a Siamese-BiLSTM model based on Siamese Network and bi-directional long short-term memory (BiLSTM) network to identify the correlation between cells, and finally constructs a logical structure tree of the table through the correlation. The experimental results show that the accuracy of this method can reach 99.2063% in header recognition and 95.0177% in correlation recognition, which is higher than other published methods.