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Current control of prosthetic hands is ineffective when grasping deformable, irregular, or heavy objects. In humans, grasping is achieved under spinal reflexive control of the musculotendon skeletal structure, which produces a hand stiffness commensurate with the task. We hypothesize that mimicking reflex on a prosthetic hand may improve grasping performance and safety when interacting with human. Here, we present a design of compliant controller for prosthetic hand with a neuromorphic model of human reflex. The model includes 6 motoneuron pools containing 768 spiking neurons, 1 muscle spindle with 128 spiking afferents, and 1 modified Hill-type muscle. Models are implemented using neuromorphic hardware with 1 kHz real-time computing. Experimental tests showed that the prosthetic hand could sustain a 40 N load compared to 95 N for an adult. Stiffness range was adjustable from 60 to 640 N/m, about 46.6% of that of human hand. The grasping velocity could be ramped up to 14.4 cm/s, or 24% of the human peak velocity. The complaint control could switch between free movement and contact force when pressing a deformable beam. The amputee can achieve a 47% information throughput of healthy humans. Overall, the reflex-enabled prosthetic hand demonstrated the attributes of human compliant grasping with the neuromorphic model of spinal neuromuscular reflex.