In this paper, we propose a low-complexity multiple-parallel-concatenated (MPC) coding scheme for magnetic recording systems, where a high-rate quasi-cyclic (QC) low-density parity-check (LDPC) code with column weight 2 based on the Balanced Incomplete Block Design (BIBD) construction is used as the component code. Simulation results show that the proposed scheme improves the error floor performance considerably as compared with previous MPC schemes with single-parity-check (MPCSPC) codes and performs comparably to structured LDPC codes over idealized partial-response channels.