As one of the important sensing technology, tactile sense has been the focus of attention in recent years. Because of its small, light, and anti-electromagnetic interference, fiber Bragg grating (FBG), as an advanced tactile sensor, can be encapsulated on any type of industrial manipulator. Based on the 3-D characteristics of the grabbed object, this article designs a three-fingers FBG tactile sensing system. The structure of wavelength-swept optical coherence tomography is built to collect high sensitivity three-channels FBG tactile sensing signal. The obtained tactile signal is 1-D small volume data, which has fast transmission rate and occupies a small bandwidth. The system is suitable for application in any places especially in industrial with complex environment and precious bandwidth. FBG tactile signal is demodulated into a time-correlation sequence representing the grasping process as the input of neural network. The classification results of two neural networks for processing time-correlation signal, such as WaveNet and long short-term memory (LSTM), are compared. For three channels of the obtained tactile signal, a squeeze-and-excitation module, which increases the correlation between channels, is added to the better performance LSTM model. The accuracy of classification is further improved. The squeeze-and-excitation LSTM (SE-LSTM) classification result shows that the classification accuracy of SE-LSTM for six types of objects with similar size and shape reaches 95.97%, which proves the effective of FBG tactile sensing technology for object classification. The time of single recognition can reach 1.2 ms, which meets the requirements of real time.