Humans can steadily and gently grasp unfamiliar objects based on tactile perception. Robots still face challenges in achieving similar performance due to the difficulty of learning accurate grasp-force predictions and force control strategies that can be generalized from limited data. In this article, we propose an approach for learning grasping from ideal force control demonstrations, to achieve similar performance of human hands with limited data size. Our approach utilizes objects with known contact characteristics to automatically generate reference force curves without human demonstrations. In addition, we design the dual convolutional neural networks (Dual-CNN) architecture which incorporats a physics-based mechanics module for learning target grasping force predictions from demonstrations. The described method can be effectively applied in vision-based tactile sensors and enables gentle and stable grasping of objects from the ground. The described prediction model and grasping strategy were validated in offline evaluations and online experiments, and the accuracy and generalizability were demonstrated.