Shape recognition plays a significant role in the field of robot perception. In view of the low efficiency and few types of shape recognition of the fiber tactile sensor applied to flexible skin, a convolutional-neural-network-based FBG tactile sensing array shape recognition method was proposed. Firstly, a sensing array was fabricated using flexible resin and 3D printing technology. Secondly, a shape recognition system based on the tactile sensing array was constructed to collect shape data. Finally, shape classification recognition was performed using convolutional neural network, random forest, support vector machine, and k-nearest neighbor. The results indicate that the tactile sensing array exhibits good sensitivity and perception capability. The shape recognition accuracy of convolutional neural network is 96.58%, which is 6.11%, 9.44%, and 12.01% higher than that of random forest, k-nearest neighbor, and support vector machine. Its F1 is 96.95%, which is 6.3%, 8.73%, and 11.94% higher than random forest, k-nearest neighbor, and support vector machine. The research of FBG shape sensing array based on convolutional neural network provides an experimental basis for shape perception of flexible tactile sensing.