The clinical syndromes of Progressive Supranuclear Palsy (PSP) may be mediated by abnormal temporal dynamics of brain networks, due to the impact of atrophy, synapse loss and neurotransmitter deficits. We tested the hypothesis that alterations in signal complexity in neural networks influence short-latency state transitions. Ninety-four participants with PSP and 64 healthy controls were recruited from two independent cohorts. All participants underwent clinical and neuropsychological testing and resting-state functional MRI. Network dynamics were assessed using hidden Markov models and neural signal complexity measured in terms of multiscale entropy. In both cohorts, PSP increased the proportion of time in networks associated with higher cognitive functions. This effect correlated with clinical severity as measured by the PSP-rating-scale, and with reduced neural signal complexity. Regional atrophy influenced abnormal brain-state occupancy, but abnormal network topology and dynamics were not restricted to areas of atrophy. Our findings show that the pathology of PSP causes clinically relevant changes in neural temporal dynamics, leading to a greater proportion of time in inefficient brain-states.