Tactile sensing is used to explore and manipulate objects, which is essential for the interaction with the environment. A novel magnetostrictive tactile sensor array for use in robotic fingers based on smart material, Fe83Ga17 alloy (Galfenol), was proposed. According to the electromagnetism theory, cantilever beam theory, and inverse magnetostrictive effect, the force measurement model of the sensor has been established. The theoretical analysis and experimental verification for the sensor have been carried out. The sensor is sensitive to the force 0–2 N, the maximum value of output voltage is 96.13 mV. We implement the feature extraction and the tactile object recognition on data acquired during an underactuated manipulator equipped with the magnetostrictive tactile sensor array. The actuator positions and tactile sensor values were considered to be available feature data. The proposed approach does not require force modulation and is suitable for gripping arbitrary initial position and orientation of object, so the tactile sensing system can be integrated into the actual robotic gripping and recognizing scenes.