Anthropomorphic robotic hands have been widely investigated to dexterously manipulate objects because of their anatomical similarity to the human hand. However, the large dimension of configuration space challenges the real-time performance of existing grasp planning methods and drastically limits the application of anthropomorphic hands. In this letter, we propose a fast force-closure grasp synthesis (FFCGS) method for the anthropomorphic hand to efficiently grasp unknown objects. The FFCGS is implemented by using a signed distance field (SDF) as input. Firstly, a network that samples feasible 6D wrist poses is trained in an end-to-end fashion to reduce the dimension of search space. Furthermore, a fast optimization algorithm is presented to find finger configurations for force-closure precision grasp based on the differentiable Q-distance metric. We validate our method in both a simulated and a real-world environment. Experiment results show that the proposed FFCGS achieves a significantly improved performance in terms of time efficiency (5 times faster), grasp quality metrics, and success rate (5%-10% improvement) over benchmark methods. The outcomes of this study have great significance in promoting the motion planning of robot hand-arm systems and upper-limb prostheses.