Restoring hand function is a top priority for individuals with tetraplegia. This challenge motivates considerable research on brain-computer interfaces (BCIs), which bypass damaged neural pathways to control paralyzed or prosthetic limbs. Here, we demonstrate the BCI control of a prosthetic hand using intracortical recordings from the posterior parietal cortex (PPC). As part of an ongoing clinical trial, two participants with cervical spinal cord injury were each implanted with a 96-channel array in the left PPC. Across four sessions each, we recorded neural activity while they attempted to press individual fingers of the contralateral (right) hand. Single neurons modulated selectively for different finger movements. Offline, we accurately classified finger movements from neural firing rates using linear discriminant analysis (LDA) with cross-validation (accuracy = 90%; chance = 17%). Finally, the participants used the neural classifier online to control all five fingers of a BCI hand. Online control accuracy (86%; chance = 17%) exceeded previous state-of-the-art finger BCIs. Furthermore, offline, we could classify both flexion and extension of the right fingers, as well as flexion of all ten fingers. Our results indicate that neural recordings from PPC can be used to control prosthetic fingers, which may help contribute to a hand restoration strategy for people with tetraplegia.