Predicting whether a particular grasp will succeed is critical to performing stable grasping and manipulating tasks. Robots need to combine vision and touch as humans do to accomplish this prediction. The primary problem to be solved in this process is how to learn effective visual-tactile fusion features. In this letter, we propose a novel Visual-Tactile Fusion learning method based on the Self-Attention mechanism (VTFSA) to address this problem. We compare the proposed method with the traditional methods on two public multimodal grasping datasets, and the experimental results show that the VTFSA model outperforms traditional methods by a margin of 5+% and 7+%. Furthermore, visualization analysis indicates that the VTFSA model can further capture some position-related visual-tactile fusion features that are beneficial to this task and is more robust than traditional methods.