In this paper, a new construction of quasi-cyclic low-density parity-check (QC-LDPC) codes for unequal error protection (UEP) is proposed. We first give a new class of UEP block codes. QC-LDPC codes with binomial-term parity-check matrices which can avoid girths less than 8 and achieve an enlarged upper bound on the minimum distance are also introduced. An effective UEP scheme based on the proposed UEP block codes and QC-LDPC codes which can provide flexible choice of protection levels is then presented. Simulation results show that the new QC-LDPC codes can achieve good performance and low error floors. The bits with different designed protection levels can indeed have unequal bit-error-rate performance.