In this paper, a novel method of active tactile perception based on 3D neural networks and a high-resolution tactile sensor installed on a robot gripper is presented. A haptic exploratory procedure based on robotic palpation is performed to get pressure images at different grasping forces that provide information not only about the external shape of the object, but also about its internal features. The gripper consists of two underactuated fingers with a tactile sensor array in the thumb. A new representation of tactile information as 3D tactile tensors is described. During a squeeze-and-release process, the pressure images read from the tactile sensor are concatenated forming a tensor that contains information about the variation of pressure matrices along with the grasping forces. These tensors are used to feed a 3D Convolutional Neural Network (3D CNN) called 3D TactNet, which is able to classify the grasped object through active interaction. Results show that 3D CNN performs better, and provide better recognition rates with a lower number of training data.