The design of LDPC decoders with low complexity, high throughput, and good performance is a critical task. A well-known strategy is to design structured codes such as quasi-cyclic LDPC (QC-LDPC) that allow partially-parallel decoders. Sequential schedules, such as Layered Belief-Propagation (LBP), converge faster than the traditional flooding schedule while allowing parallel decoding of QC-LDPC codes. In this paper, we propose a novel low-complexity sequential schedule called Zigzag LBP (Z-LBP). Current LBP schedules do not allow partially-parallel architectures in the regime of high-rate codes with small-to-medium blocklengths. Our proposed algorithm can still be implemented in a partially-parallel manner in this regime. Z-LBP provides the same benefits as LBP including faster convergence speed and lower frame error rates than flooding.